Question

Question (CLO 4, Marks 4): Aquant jock from your firm used a linear specification to estimate the Sales for its product and sent you a hard copy of the results. Based on these estimates,

Write an equation that summarizes the demand for the firm’s product.

Which regression coefficients are statistically significant at the 5 percent level?

Comment on how well the regression line fits the data.

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.38

R Square

0.14

Adjusted R Square

0.13

Standard Error

20.77

Observations

150

Analysis of Variance

Degrees of Freedom

Sum of Squares

Mean Square

F

Significance F

Regression

2

10,398.87

5199.43

12.05

0.00

Residual

147

63,408.62

431.35

Total

149

73,807.49

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

58.87

15.33

3.84

0.00

28.59

89.15

Price of X

-1.64

0.85

-1.93

0.06

-3.31

0.04

Income (‘000s)

1.11

0.24

4.64

0.00

0.63

1.56

Answer 1

The OLS regression result provided in the question is:

Regression Statistics
Multiple R	0.38
R Square	0.14
Adjusted R Square	0.13
Standard Error	20.77
Observations	150
Analysis of Variance
	Degrees of Freedom	Sum of Squares	Mean Square	F	Significance F
Regression	2	10398.87	5199.43	12.05	0
Residual	147	63408.62	431.35
Total	149	73807.49
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	58.87	15.33	3.84	0	28.59	89.15
Price of X	-1.64	0.85	-1.93	0.06	-3.31	0.04
Income (‘000s)	1.11	0.24	4.64	0	0.63	1.56

The OLS regression equation is:

PredictedSales = 58.87 - 1.64*Price of X + 1.11*Income('000s)

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It shall be noted that the regression coefficient of the explanatory variable "Income('000s) has the t-statistic of 4.64 with the actual p-value of 0, which is less than a critical p-value of 0.05 at a 5% level of significance.

This indicates that the variable Income('000s) is statistically significant at 5% level of significance

Whereas, the regression coefficient of explanatory variable "Price of X" has the t-statistic of -1.93 with the p-value of 0.06, which is greater than a critical p-value of 0.05 at a 5% level of significance.

This indicates that the variable Price of X is not statistically significant at 5% level of significance.

Thus, the variable Income('000s) is statistically significant at 5% level of significance

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The R-squared of the given regression model is 0.14, which is 14% which is also termed as the coefficient of determination.

It is considered as a measure of goodness-of-fit of the OLS regression model.

It shows that only 14% of the variation in the Sales is explained by the model that has only two explanatory variables - Price of X and Income('000s)

Thus, the goodness-of-fit of the model is quite low.