Data location fooddécorservicesummated ratingcoded locationcostcity2

1. DATALocationFoodDécorServiceSummated RatingCoded
LocationCostCity21192060062City24242068067City221414500
23City27232474079City20131952032City19111848038City2123
2064046City19171955043City21161956039City16151748043Cit
y20261965044City23151755029City22232166059City21162057
056City19161853032City25222269056City22121751023City211
21649040City22192061045City17151951044City23182162040C
ity21172058033City23232167057City19171753043City2216195
7049City21202061028City19161651035City24202468079City19
181754042City19111242021City23161857040City19202362049
City19181855045City23202164054City25212268064City202017
57048City18141749041City24192063034City22242167053City1
8151750027City22172160044City23202265058City2119216106
8City22262068059City18181854061City23172060059City22141
854048City24242573078City19211858065City20151954042Sub
urban22172160153Suburban22182161145Suburban20131750139
Suburban21162057143Suburban24192063144Suburban1916165
1129Suburban22222165137Suburban23162059134Suburban181
91956133Suburban18171752137Suburban22172261154Suburba
n22172059130Suburban19221758149Suburban21121952144Sub
urban15201651134Suburban22202264155Suburban20181856148
Suburban18161852136Suburban22162159129Suburban2221236
6140Suburban19191957138Suburban24182062138Suburban252
12470155Suburban24212065143Suburban20131750133Suburba
n18191855144Suburban22151956141Suburban18152053145Sub
urban23252169141Suburban20222264142Suburban20191756137
Suburban24192265156Suburban24272475160Suburban2118216
0146Suburban17141849131Suburban23152260135Suburban242
12166168Suburban25172264140Suburban21192060151Suburba
n23122459132Suburban21151955128Suburban19191856144Sub
urban26131857126Suburban19182057142Suburban21111648137
Suburban27202370163Suburban24202064137Suburban1911164
6122Suburban23212064153Suburban24182264162

2. Regression Analysis
using Excel 2007
MTH 305 Statistics
Data Needed in Regression AnalysisAt least two variables that
have information about several observations
Only one variable will be defined as the Y variable. There can
be one or more X variables in regression analysis.Observation
IDVariable 1Variable 2123
Data ExampleFor example, we are interested in analyzing the
linear relationship between amount of sugar and calories in a
box of cereals. We are testing whether sugar amount causes

3. calories amount. In Excel the dataset will look like…see next
slide
Data Example
Ways to Check Linear Relationship
Scatter Plot between Y and X
Correlation Value
Regression Analysis
SCATTER PLOT
Scatter-plot of Two variablesSelect the data of two variables
t
“scatter plot”Example from data above:
Looks like there is no linear relationshiip!!!
CORRELATION COEFFICIENT
Correlation Value in ExcelIn any Excel cell, type:
=CORREL(range of Y data, range of X data)For example, for
the dataset above (cereal data) where Y data are in cells B2

4. through B19 and X data are in cells C2 through C19, we will
type:
=CORREL(B2:B19, C2:C19)
The result of 0.2296 shows that there is a weak relationship
between those variables.
REGRESSION ANALYSIS
Regression Analysis
Excel Output: Intercept and Slope
The regression equation is:Regression StatisticsMultiple
R0.76211R Square0.58082Adjusted R Square0.52842Standard
Error41.33032Observations10ANOVA
dfSSMSFSignificance
FRegression118934.934818934.934811.08480.01039Residual81
3665.56521708.1957Total932600.5000CoefficientsStandard
Errort StatP-valueLower 95%Upper
95%Intercept98.2483358.033481.692960.12892-
35.57720232.07386Square
Feet0.109770.032973.329380.010390.033740.18580

5. Excel Output: R-squared
58.08% of the variation in house prices is explained by
variation in square feet
Regression StatisticsMultiple R0.76211R
Square0.58082Adjusted R Square0.52842Standard
Error41.33032Observations10ANOVA
dfSSMSFSignificance
FRegression118934.934818934.934811.08480.01039Residual81
3665.56521708.1957Total932600.5000CoefficientsStandard
Errort StatP-valueLower 95%Upper
95%Intercept98.2483358.033481.692960.12892-
35.57720232.07386Square
Feet0.109770.032973.329380.010390.033740.185 80

6. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Excel Output: Standard Error Regression StatisticsMultiple
R0.76211R Square0.58082Adjusted R Square0.52842Standard
Error41.33032Observations10ANOVA
dfSSMSFSignificance
FRegression118934.934818934.934811.08480.01039Residual81
3665.56521708.1957Total932600.5000CoefficientsStandard
Errort StatP-valueLower 95%Upper
95%Intercept98.2483358.033481.692960.12892-
35.57720232.07386Square
Feet0.109770.032973.329380.010390.033740.18580
To Plot Regression Line
Under the Regression window, place a mark
“Line Fit Plots”
Regression LineHouse price model: scatter plot and regression
line

7. Slope
= 0.10977
Intercept
= 98.248
Chart21400160017001875110015502350245014251700
House Price
Square Feet
House Price ($1000s)
245
312
279
308
199
219
405
324
319
255
Sheet4SUMMARY OUTPUTRegression StatisticsMultiple
R0.76211R Square0.58082Adjusted R Square0.52842Standard
Error41.33032Observations10ANOVAdfSSMSFSignificance
FRegression118934.934818934.934811.084760.01039Residual8
13665.56521708.1957Total932600.5000CoefficientsStandard
Errort StatP-valueLower 95%Upper
95%Intercept98.2483358.033481.692960.12892-
35.57720232.07386Square
Feet0.109770.032973.329380.010390.033740.18580RESIDUAL
OUTPUTObservationPredicted House
PriceResiduals1251.9231625835-
6.92316258352273.876710149538.12328985053284.853483932
5-
5.85348393254304.06283805283.93716194725218.9928412345-
19.99284123456268.388323258-
49.3883232587356.202513522148.79748647798367.179287305
1-

8. 43.17928730519254.667356029364.332643970710284.8534839
325-29.8534839325
Sheet414001400160016001700170018751875110011001550155
023502350245024501425142517001700
House Price
Predicted House Price
Square Feet
House Price
Square Feet Line Fit Plot
245
0
312
0
279
0
308
0
199
0
219
0
405
0
324
0
319
0
255
0
Sheet1House PriceSquare
Feet2451400312160027917003081875199110021915504052350
324245031914252551700
Sheet10000000000
House Price
Square Feet
House Price

9. 0
0
0
0
0
0
0
0
0
0
Sheet2
Sheet3
MULTIVARIATE REGRESSION
Multivariate Regression
Multivariate = two or more X variables than influence YScatter -
Plot: get them separately for each pair of X and Y.Correlation
Coefficient: compute them separately for each pair of X and
Y.Regression Analysis: If we want to analyze how two or more
X variables have an impact on Y, then we will do the same as
above for the case of one X but select the data in all the X
variables at the same time.
feet)
(square
0.10977
98.24833

10. price
house
+
=
0.58082
32600.5000
18934.9348
SST
SSR
r
2
=
=
=
0.03297
S
1
b
=
0
50
100
150
200
250
300
350
400
450
050010001500200025003000
Square Feet
House Price ($1000s)
feet)

11. (square
0.10977
98.24833
price
house
+
=
ProductCaloriesSugar (grams)
Kellogg's20018
Sam's Choice Extra raisin (Wal-Mart)21023
Kountry Fresh (Winn-Dixie)17017
Post Premium19020
American Fare (kmart)17017
America's Choice (A&P)20018
Safeway20018
Kroger20018
General Mills Total18019
Post The Original Shredded Wheat 'N Bran2001
Post The Original Shredded Wheat, Spoon Size1700
Kellogg's Raisin Squares Mini-Wheats18012
Healthy Choice Toasted Brown Sugar Squares1909
Kountry Fresh Frosted Bite Size (Winn-Dixie)20011
Post Frosted Bite Size19012
Kroger Frosted Bite Size19011
Kellogg's Frosted Mini-Wheats20012
Safeway Frosted Bite Size19011
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.

12. Chap 13-*
Chapter 13
Regression Analysis:
PART 1: Simple Linear Regression
Basic Business Statistics
10th Edition
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Learning Objectives
In this chapter, you learn: How to use regression analysis to
predict the value of a dependent variable (Y) based on an
independent variable (X): X causes YHow to evaluate the
assumptions of regression analysis and know what to do if the
assumptions are violatedTo make inferences about the slope in a
linear regression (linear relation b/w X and Y)To estimate mean
values and predict individual values
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Analysis when Two Variables are Related
A scatter diagram can be used to show the relationship between
two variables
Scatter diagrams were first presented in Ch. 2
Correlation analysis is used to measure strength of the
association (linear relationship) between two variables (Ch.
3)Correlation is only concerned with strength of the relationship
No causal effect is implied with correlation

13. Regression analysis is used to show causation
Changes in X cause changes in Y
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Correlation Coefficient (r)–1 < r < 1The closer to –1, the
stronger the negative linear relationshipThe closer to 1, the
stronger the positive linear relationshipThe closer to 0, the
weaker the linear relationship
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 3-*
Scatter Plots of Data with Various Correlation Coefficients
Y
X

14. Y
X
Y
X

15. Y
X
Y
X
r = -1
r = -.6
r = 0
r = +.3
r = +1
Y
X
r = 0
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.

16. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Introduction to
Regression AnalysisRegression analysis is used to:Explain the
impact of changes in an independent variable on changes in the
dependent variablePredict the value of a dependent variable
based on the value of one or more independent variables
Dependent variable (Y): the variable we wish to predict or
explain
Independent variable (X): the variable used to explain the
dependent variable
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Simple Linear Regression ExampleA real estate agent wishes to
examine the relationship between the selling price of a home
and its size (measured in square feet)
Dependent variable (Y) = house priceIndependent variable (X) =
square feet
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Sample Data for House Price ModelHouse Price
(Y)Square Feet
(X)24514003121600279170030818751991100219155040523503
24245031914252551700

17. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Types of Relationships
Y
X

18. Y
X
Y

19. Y
X
X
Linear relationships
Non-linear relationships
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Simple Linear Regression ModelOnly one independent variable,
XRelationship between X and Y is described by a linear
function:
Y = intercept + slope(X)
Y = a + bXChanges in Y are assumed to be caused by
changes in X
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*

20. Linear Relationships
Y
X
Y
X

21. Y
Y
X
X
Strong relationships
Weak relationships

22. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Linear Relationships
Y
X

23. Y
X
No relationship
(continued)
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Linear component
Simple Linear Regression Model
Population
Y intercept
Population Slope
Coefficient
Random Error term
Dependent Variable
Independent Variable
Random Error
component
Population Parameters
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.

24. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
The simple linear regression equation provides an estimate of
the population regression line
Sample Statistics:
Regression Equation
Estimate of the regression
intercept
Estimate of the regression slope
Estimated (or predicted) Y value for observation i
Value of X for observation i
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Formulas: Slope and Intercept
Slope:
b1 =
Intercept:
b0 =
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.

25. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*INTERCEPT: b0 is the estimated average value of Y
when the value of X is zero
SLOPE: b1 is the estimated change in the average value of Y as
a result of a one-unit change in X
Interpretation of the
Slope and the Intercept
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Simple Linear Regression ExampleA real estate agent wishes to
examine the relationship between the selling price of a home
and its size (measured in square feet)
A random sample of 10 houses is selectedDependent variable
(Y) = house price in $1000sIndependent variable (X) = square
feet
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Sample Data for House Price ModelHouse Price in $1000s
(Y)Square Feet
(X)24514003121600279170030818751991100219155040523503
24245031914252551700

26. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Graphical PresentationHouse price model: scatter plot
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chart21400160017001875110015502350245014251700
House Price
Square Feet
House Price ($1000s)
245
312
279
308
199
219
405
324
319
255

27. Sheet4SUMMARY OUTPUTRegression StatisticsMultiple
R0.76211R Square0.58082Adjusted R Square0.52842Standard
Error41.33032Observations10ANOVAdfSSMSFSignificance
FRegression118934.934818934.934811.084760.01039Residual8
13665.56521708.1957Total932600.5000CoefficientsStandard
Errort StatP-valueLower 95%Upper
95%Intercept98.2483358.033481.692960.12892-
35.57720232.07386Square
Feet0.109770.032973.329380.010390.033740.18580RESIDUAL
OUTPUTObservationPredicted House
PriceResiduals1251.9231625835-
6.92316258352273.876710149538.12328985053284.853483932
5-
5.85348393254304.06283805283.93716194725218.9928412345-
19.99284123456268.388323258-
49.3883232587356.202513522148.79748647798367.179287305
1-
43.17928730519254.667356029364.332643970710284.8534839
325-29.8534839325
Sheet414001400160016001700170018751875110011001550155
023502350245024501425142517001700
House Price
Predicted House Price
Square Feet
House Price
Square Feet Line Fit Plot
245
0
312
0
279
0
308
0
199
0

28. 219
0
405
0
324
0
319
0
255
0
Sheet1House PriceSquare
Feet2451400312160027917003081875199110021915504052350
324245031914252551700
Sheet10000000000
House Price
Square Feet
House Price
0
0
0
0
0
0
0
0
0
0
Sheet2
Sheet3
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Regression Using ExcelData / Data Analysis / Regression
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.

29. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Excel Output
The regression equation is:Regression StatisticsMul tiple
R0.76211R Square0.58082Adjusted R Square0.52842Standard
Error41.33032Observations10ANOVA
dfSSMSFSignificance
FRegression118934.934818934.934811.08480.01039Residual81
3665.56521708.1957Total932600.5000CoefficientsStandard
Errort StatP-valueLower 95%Upper
95%Intercept98.2483358.033481.692960.12892-
35.57720232.07386Square
Feet0.109770.032973.329380.010390.033740.18580
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Graphical PresentationHouse price model: scatter plot and
regression line

30. Slope
= 0.10977
Intercept
= 98.248
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chart21400160017001875110015502350245014251700
House Price
Square Feet
House Price ($1000s)
245
312
279
308
199
219
405
324
319
255
Sheet4SUMMARY OUTPUTRegression StatisticsMultiple
R0.76211R Square0.58082Adjusted R Square0.52842Standard
Error41.33032Observations10ANOVAdfSSMSFSignificance
FRegression118934.934818934.934811.084760.01039Residual8
13665.56521708.1957Total932600.5000CoefficientsStandard
Errort StatP-valueLower 95%Upper
95%Intercept98.2483358.033481.692960.12892-
35.57720232.07386Square
Feet0.109770.032973.329380.010390.033740.18580RESIDUAL
OUTPUTObservationPredicted House
PriceResiduals1251.9231625835-
6.92316258352273.876710149538.12328985053284.853483932
5-
5.85348393254304.06283805283.93716194725218.9928412345-
19.99284123456268.388323258-
49.3883232587356.202513522148.79748647798367.179287305

31. 1-
43.17928730519254.667356029364.332643970710284.8534839
325-29.8534839325
Sheet414001400160016001700170018751875110011001550155
023502350245024501425142517001700
House Price
Predicted House Price
Square Feet
House Price
Square Feet Line Fit Plot
245
0
312
0
279
0
308
0
199
0
219
0
405
0
324
0
319
0
255
0
Sheet1House PriceSquare
Feet2451400312160027917003081875199110021915504052350
324245031914252551700
Sheet10000000000
House Price
Square Feet

32. House Price
0
0
0
0
0
0
0
0
0
0
Sheet2
Sheet3
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Interpretation of the
Intercept, b0b0 is the estimated average value of Y when the
value of X is zero (if X = 0 is in the range of observed X
values)Here, no houses had 0 square feet, so b0 = 98.24833 just
indicates that, for houses within the range of sizes observed,
$98,248.33 is the portion of the house price not explained by
square feet
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.

33. Chap 13-*
Interpretation of the
Slope Coefficient, b1b1 measures the estimated change in the
average value of Y as a result of a one-unit change in XHere, b1
= .10977 tells us that the average value of a house increases by
.10977($1000) = $109.77, on average, for each additional one
square foot of size
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Predict the price for a house with 2000 square feet:
The predicted price for a house with 2000 square feet is
317.85($1,000s) = $317,850
Predictions using
Regression Analysis
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*The coefficient of determination is the portion of the
total variation in the dependent variable that is explained by
variation in the independent variableThe coefficient of
determination is also called R-squared and is denoted as r2
(also, R2)
Coefficient of Determination (r2)

34. note:
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
r2 = 1
Examples of Approximate
r2 Values
Y
X
Y
X
r2 = 1
r2 = 1
Perfect linear relationship between X and Y:
100% of the variation in Y is explained by variation in X

35. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Examples of Approximate
r2 Values
Y
X

36. Y
X
0 < r2 < 1
Weaker linear relationships between X and Y:
Some but not all of the variation in Y is explained by variation
in X
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Examples of Approximate
r2 Values
r2 = 0
No linear relationship between X and Y:
The value of Y does not depend on X. (None of the variation in
Y is explained by variation in X)

37. Y
X
r2 = 0
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
R-squared from Excel Output
58.08% of the variation in house prices is explained by
variation in square feet
Regression StatisticsMultiple R0.76211R
Square0.58082Adjusted R Square0.52842Standard
Error41.33032Observations10ANOVA
dfSSMSFSignificance
FRegression118934.934818934.934811.08480.01039Residual81
3665.56521708.1957Total932600.5000CoefficientsStandard
Errort StatP-valueLower 95%Upper
95%Intercept98.2483358.033481.6929 60.12892-
35.57720232.07386Square

38. Feet0.109770.032973.329380.010390.033740.18580
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Assumptions of Regression
Use the acronym LINE:LinearityThe underlying relationship
between X and Y is linearIndependence of ErrorsError values
are statistically independentNormality of ErrorError values (ε)
are normally distributed for any given value of XEqual
Variance (Homoscedasticity)The probability distribution of the
errors has constant variance
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Hypothesis testing about the Slope: t Testt test for a population
slopeIs there a linear relationship between X and Y?Null and
alternative hypotheses
H0: β1 = 0 (no linear relationship)
(linear relationship does exist)Test statistic

39. where:
b1 = regression slope
coefficient
β1 = hypothesized slope
Sb = standard
error of the slope
1
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Standard Error
of the SlopeThe standard error of the regression sl ope
coefficient (b1) is estimated by
where:
= Estimate of the standard error of the least squares slope
= Standard error of the estimate
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*

40. Standard Error from
Excel OutputRegression StatisticsMultiple R0.76211R
Square0.58082Adjusted R Square0.52842Standard
Error41.33032Observations10ANOVA
dfSSMSFSignificance
FRegression118934.934818934.934811.08480.01039Residual81
3665.56521708.1957Total932600.5000CoefficientsStandard
Errort StatP-valueLower 95%Upper
95%Intercept98.2483358.033481.692960.12892-
35.57720232.07386Square
Feet0.109770.032973.329380.010390.033740.18580
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Simple Linear Regression Equation:
The slope of this model is 0.1098
Does square footage of the house affect its sales price at 95%
CL?
Hypothesis testing about the Slope: t TestHouse Price
(y)Square Feet
(x)24514003121600279170030818751991100219155040523503
24245031914252551700

41. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Example
H0: β1 = 0
From Excel output:
t
b1
(continued)CoefficientsStandard Errort StatP-
valueIntercept98.2483358.033481.692960.12892Square
Feet0.109770.032973.329380.01039

42. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Critical Value for t statistic
Use “t” table on page 814-815
Depends on:
degrees of freedom: df = n – 2
Significance level: �95% CL has � = 0.0590% CL has � = 0.10
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 13-*
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.
Chap 8-*
t Table (p. 814-815)
Upper Tail Area
df
.25

43. …
Sheet2House PriceSquare feet24514003121600SUMMARY
OUTPUT27917003081875Regression Statistics1991100Multiple
R0.76211371322191550R
Square0.58081731194052350Adjusted R
Square0.52841947593242450Standard
Error41.33032365033191425Observations102551700ANOVAdf
SSMSFSignificance
FRegression118934.93477569218934.93477569211.0847576166
0.0103940164Residual813665.5652243081708.1956530385Tota
l932600.5CoefficientsStandard Errort StatP-valueLower
95%Upper 95%Lower 95.0%Upper
95.0%Intercept98.248329621458.03347858471.69295951260.12
89188121-35.5771118647232.0737711075-
35.5771118647232.0737711075Square
feet0.10976773780.03296944333.32937796240.01039401640.03
374006540.18579541030.03374006540.1857954103RESIDUAL
OUTPUTObservationPredicted House
PriceResiduals1251.9231625835-
6.92316258352273.876710149538.12328985053284.853483932
5-
5.85348393254304.06283805283.93716194725218.9928412345-
19.99284123456268.388323258-
49.3883232587356.202513522148.79748647798367.179287305
1-
43.17928730519254.667356029364.332643970710284.8534839
325-29.8534839325
Square feet Line Fit Plot
House Price 1400 1600 1700 1875 1100 1550 2350 2450 1425
1700 245 312 279 308 199 219 405 324 319 255
Predicted House Price 1400 1600 1700 1875 1100 1550
2350 2450 1425 1700 251.92316258351892
273.87671014953867 284.8534839325485
304.06283805281578 218.99284123448933

44. 268.38832325803372 356.20251352211261
367.1792873051225 254.66735602927139
284.8534839325485
Square feet
House Price
Sheet3