[Part A: Module III Problem Set]

1. [1 pt]Which of the following is not true about the regression model?

(a)	In the regression model, the residual of each observation represents the deviation from the least squared regression line. In other words, it represents the difference between the actual and predicted values.
(b)	In the ideal situation, errors in the population regression model follow a normal distribution with zero mean.
(c)	The errors in the regression model should be independent of each other.
(d)	When building a regression model to estimate the effect of advertising on sales, the larger the slope is, the more significant the impact of the variable is independent of its p-value.

2. Which of the following is true in the context of using regression analysis to estimate relationships?

(a)	If the intercept coefficient is statistically significant, it means the average value of the dependent variable is almost close zero when the independent variable is zero.
(b)	If the slope coefficient is statistically significant and positive, it means that we have evidence that an increase in the independent variable is associated with a negative change in the dependent variable.
(c)	The higher (in absolute value) the slope coefficient for an independent variable is, the lower the p-value for that variable will be.
(d)	If the p-value of the F -statistic is small, it means that there is significant statistical evidence that variation in the dependent variable are well explained by variations in the independent variables.

3. [Family Friendly Business Practices] Increasingly, some firms have started practicing various family-friendly practices, such as on-site daycare for children, ability to tele-commute and work from home, availability of leave for family reasons, etc. Are such policies rewarded by investors in the stock market? To test this, 13 public companies were examined. For each, a Family Friendliness Index (FFI) was computed based on the different family-friendly practices they had. Additionally, their excess returns (compared to the S&P 500) over the past 5 years were also computed. A simple regression model was then estimated with the excess returns as the dependent variable, and FFI as the independent variable. A partial output of the regression is given below.

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.621

R Square F

Adjusted R Square 0.329

Standard Error G

Observations 13

ANOVA

df SS MS F Significance F

Regression 1 15.115 15.115 6.894 H

Residual D E 2.193

Total

12

39.233

	Coefficients	Standard Error	t Stat	Pvalue	Lower 95%	Upper 95%
Intercept	3.111	1.267	2.455	0.032	5.900	0.322
X Variable 1	0.068	0.026	A	B	C

A=

(a)	0.382
(b)	0.407
(c)	2.455
(d)	2.615

4. B=

(a)	0.004
(b)	0.009
(c)	0.012
(d)	0.024

5. C=

(a)	0.006
(b)	0.008
(c)	0.011
(d)	0.170

6. D=

(a)	1
(b)	11
(c)	12
(d)	13

7. E=

(a)	24.12
(b)	24.12
(c)	26.31
(d)	54.35

8. F=

(a)	0.212
(b)	0.385
(c)	0.615
(d)	0.788

9. G=

(a)	1.481
(b)	1.808
(c)	2.193
(d)	4.911

10. What would you conclude from the F-test for this output? Recall that the p-value of the F-test appears in the box marked H. There is only one independent variable, so the F-test reproduces something you have already done.

(a)	Do not reject the null hypothesis that the slope coefficient is zero at either the 1% or 5% levels of significance
(b)	Reject the null hypothesis that the slope coefficient is zero at the 5% but not the 1% level of significance.
(c)	Reject the null hypothesis that the slope coefficient is zero at that 1% but not at the 5% level of significance.
(d)	Reject the hypothesis that the slope coefficient is zero at both the 1% and 5% levels of significance.