1. A linear regression model was estimated to relate the number of cars sold (dependent variable) to the number of TV ads (independent variable) based on weekly data from 5 weeks. 2. The regression results show that the number of TV ads has a statistically significant impact on car sales based on the F-test and t-tests. 3. The estimated regression equation found that for every additional TV ad, car sales are predicted to increase by 5 units on average, with an intercept of 10 cars sold even without any TV ads.

1. By C. Chen

2. which requires
&
x  E ( x) x TVC  aQ  bQ 2  cQ 3
zx  
x 
n SMC  a  2bQ  3cQ 2

4. I prefer to take face to face I prefer to teach face to face
course. course.
The materials are too Aren’t they easy enough?
tough for me.
I am not good at math. They just don’t like math.
Quantitative analysis is Quantitative analysis is
useless; why I need to useful; why they don’t
learn it? study it?
Professor is really mean. Students are really lazy.

5. Camtasia

8. Managerial Economics
Demand Estimation (Time
Series)
A linear trend equation for sales of the form
Qt = a + bt
was estimated for the period 1996– 2010 ( i. e., t =1 for 1996, t = 2 for 1997, . . .
). The results of the regression are as follows:
DEPENDENT VARIABLE: QT R- SQUARE F- RATIO P- VALUE ON F
OBSERVATIONS: 15 0.6602 25.262 0.0002
PARAMETER STANDARD
VARIABLE ESTIMATE ERROR T- RATIO P- VALUE
INTERCEPT 73.71460 34.08 2.16 0.0498
t 3.7621 0.7490 5.02 0.0002
a. Evaluate the statistical significance of the estimated coefficients. (Use 5
percent for the significance level.) Does this estimation indicate a significant
trend?
b. Using this equation, forecast sales in 2011 and 2020.
Dr. C. Chen

9. A linear trend equation for sales of the form
Qt = a + bt
was estimated for the period 1996– 2010 ( i. e., t =1 for1996, t = 2 for1997, . . .). The results
of the regression are as follows:
DEPENDENT VARIABLE: QT R- SQUARE F- RATIO P- VALUE ON F
OBSERVATIONS: 15 0.6602 25.262 0.0002
PARAMETER STANDARD
VARIABLE ESTIMATE ERROR T- RATIO P- VALUE
INTERCEPT 73.71460 34.08 2.16 0.0498
t 3.7621 0.7490 5.02 0.0002
a. Evaluate the statistical significance of the estimated coefficients. (Use 5 percent for the
significance level.) Does this estimation indicate a significant trend?
The p-value of t-test is 0.0002<0.05. The trend significance is confirmed. The p-value of F-
test is also less than 0.05, we can apply the model for future period prediction.
b. Using this equation, forecast sales in 2011 and 2020.
Year 2011 (t =16), Q = 73.7146 + 3.7621(16) = 133.9082
Year 2020 (t =25), Q = 73.7146 + 3.7621(25) = 167.7671
Dr. C. Chen

11. Excel’s Regression Tool
 Excel Value Worksheet
A B C D E F G H I
1 Week TV Ads Cars Sold
2 1 1 14
3 2 3 24
4 3 2 18
5 4 1 17 Data
6 5 3 27
7
8 SUMMARY OUTPUT
9 Regression Statistics Output
10 Regression Statistics
11 Multiple R 0.936585812
12 R Square 0.877192982
13
14
Adjusted R Square
Standard Error
0.83625731
2.160246899
ANOVA Output Estimated Regression
15 Observations 5 Equation Output
16
17 ANOVA
18 df SS MS F Significance F
19 Regression 1 100 100 21.42857 0.018986231
20 Residual 3 14 4.666667
21 Total 4 114
22
23 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
24 Intercept 10 2.366431913 4.225771 0.024236 2.468950436 17.53104956 2.468950436 17.53104956
25 TV Ads 5 1.08012345 4.6291 0.018986 1.562561893 8.437438107 1.562561893 8.437438107
26