1. (5 points) Facts about correlation. Answer the following questions about correlation (r). a. What is the strongest the correlation can ever be? b. If there is no relationship, r is equal to c. The correlation coefficient ranges from __________to __________ d. If the points fall in an almost perfect, negative linear pattern, r is close to: __________ e. If the points fall in an almost perfect, positive linear pattern, r is close to: __________ 2. (6 points) Relationship between Height and Weight. Data has been collected on 219 STAT 200 students. Weight is measured in pound and Height in inch. Below are some descriptive statistics of Weight and Height. Then a linear regression was performed on height and weight. The output looks as follows: a. Write the regression equation based on the output. b. What is the response variable (dependent variable) and what is the predictor (independent variable)? c. Based on the equation, what is the slope? Please explain slope as the change in Y per unit change in X in the context of the variables used in this problem. d. Based on the output, what is the test of the slope for this regression equation? That is, provide the null and alternative hypotheses, the test statistic, p-value of the test, and state your decision and conclusion. e. Assume a student is 65 inch tall. Is it possible to predict his weight based on this analysis? If so, please estimate his weight using the regression equation. f. What do the Fitted (predicted) values and Residuals represent? For example, there is one record in the data set with height = 54 and weight = 110. Please use these numbers to explain what is the fitted value and what is the residual. 3. (11 points) Parts B, D are worth 2 points. Parts C, E are worth 3 points (2 plots and a conclusion for each) Relationship between eighth grade IQ and ninth grade math score. For a statistics class project, students examined the relationship between x = 8th grade IQ and y = 9th grade math scores for 20 students. The data are displayed below. Student Math Score IQ Abstract Reas 1 33 95 28 2 31 100 24 3 35 100 29 4 38 102 30 5 41 103 33 6 37 105 32 7 37 106 34 8 39 106 36 9 43 106 38 10 40 109 39 11 41 110 40 12 44 110 43 13 40 111 41 14 45 112 42 15 48 112 46 16 45 114 44 17 31 114 41 18 47 115 47 19 43 117 42 a. Create a scatter plot of the measurements by selecting Math Score for the y-axis (response) and IQ for the x-axis (predictor). Describe the relationship between math score and IQ. Minitab Users: Graph > Scatter Plot > Simple. SPSS Users: Graphs > Legacy Dialogues > Scatter/Dot > Simple Scatter b. Perform a linear regression with the Response (dependent variable) math score and the variable IQ as the Predictor (independent variable).Store/Save the (unstandardized) Residuals and Fitted(Predicted) values. These will be stored in the fourth and fifth columns of the data worksheet. What is the regression equation? What is the interpretation of R-square (just ...

1. 1. (5 points)
Facts about correlation.
Answer the following questions about correlation (r).
a. What is the strongest the correlation can ever be?
b. If there is no relationship, r is equal to
c. The correlation coefficient ranges from __________to
__________
d. If the points fall in an almost perfect, negative linear pattern,
r is close to: __________
e. If the points fall in an almost perfect, positive linear pattern,
r is close to: __________
2. (6 points)
Relationship between Height and Weight.
Data has been collected on 219 STAT 200 students. Weight is
measured in pound and Height in inch. Below are some
descriptive statistics of Weight and Height.
Then a linear regression was performed on height and weight.
The output looks as follows:
a. Write the regression equation based on the output.
b. What is the response variable (dependent variable) and what
is the predictor (independent variable)?
c. Based on the equation, what is the slope? Please explain
slope as the change in Y per unit change in X in the context of
the variables used in this problem.
d. Based on the output, what is the test of the slope for this
regression equation? That is, provide the null and alternative
hypotheses, the test statistic, p-value of the test, and state your
decision and conclusion.
e. Assume a student is 65 inch tall. Is it possible to predict his
weight based on this analysis? If so, please estimate his weight
using the regression equation.

2. f. What do the Fitted (predicted) values and Residuals
represent? For example, there is one record in the data set with
height = 54 and weight = 110. Please use these numbers to
explain what is the fitted value and what is the residual.
3. (11 points) Parts B, D are worth 2 points. Parts C, E are
worth 3 points (2 plots and a conclusion for each)
Relationship between eighth grade IQ and ninth grade math
score.
For a statistics class project, students examined the relationship
between x = 8th grade IQ and y = 9th grade math scores for 20
students. The data are displayed below.
Student
Math Score
IQ
Abstract Reas
1
33
95
28
2
31
100
24
3
35
100
29
4
38
102
30
5
41
103
33

3. 6
37
105
32
7
37
106
34
8
39
106
36
9
43
106
38
10
40
109
39
11
41
110
40
12
44
110
43
13
40
111
41
14
45
112
42

4. 15
48
112
46
16
45
114
44
17
31
114
41
18
47
115
47
19
43
117
42
a. Create a scatter plot of the measurements by selecting Math
Score for the y-axis (response) and IQ for the x-axis (predictor).
Describe the relationship between math score and IQ.
Minitab Users: Graph > Scatter Plot > Simple.
SPSS Users: Graphs > Legacy Dialogues > Scatter/Dot > Simple
Scatter
b. Perform a linear regression with the Response (dependent
variable) math score and the variable IQ as the Predictor
(independent variable).Store/Save the (unstandardized)
Residuals and Fitted(Predicted) values. These will be stored in
the fourth and fifth columns of the data worksheet.
What is the regression equation?
What is the interpretation of R-square (just use the latest
output) and how to calculate correlation based on it?

5. c. One of the students with a high IQ (number 17) appears to be
an outlier. With a sample size of only 20 this can affect our
normality assumption. Also, the constant variance assumption
could be compromised. We can visually check for constant
variance using a Residual Plot and test for normality using a
Probability Plot (or Q-Q plot).
To get a residual plot, simply create a Scatterplot using the
Residuals as the y-variable and the Fitted(Predicted) Values as
the x-variable. (Remember these should have been stored/saved
when you first performed the regression per instructions above.
If not, re-run regression and click store/save and click the boxes
for unstandardized residuals and fits(predicted) values.) Now
create a probability plot (Q-Q plot if using SPSS) of the
residuals.
Based on these two graphs and what you have learned about
hypothesis testing, what interpretations do you come to
regarding the assumptions of constant variance and normality?
Minitab Users: Probability plot go to Graphs > Probability Plot
> Single and select Residuals
SPSS Users: Q-Q plot with normal test go to Analyze >
Descriptive Statistics > Explore and enter Unstandardized
Residuals in Dependent List click Plots and select box for
Normal plots with tests
d. Although outliers should never be deleted without a reason,
there are several reasons why it may be legitimate to conduct an
analysis without them. Delete the data point for row 17 (click
on the cell with the IQ of 114, enter * and then click on any
other cell - this “enters” the asterisk in that previous cell. ) and
re-calculate the regression line for the remainder of the data.
What is the regression equation with the rest of the data?
What is the R2 and correlation between Math Score and IQ with
the outlier removed?
e. How does the fit of the regression line of the original data
(i.e. with outlier) compare (visually and statistically) to the fit
of the regression line to the data with the outlier removed?

6. Compare the fit of the regression line between the two sets of
data. Pay particular attention to the differences in R2, the slope
and how the line fits each set of data. Repeat theresidual plot
and probability plot!