Question

Input the data below into a multivariate regression into excel. Using the data generated, answer the following questions.

1. Interpret the R^2 in a sentence.

2. At an approximate 95% level of confidence, can you conclude that price offsets sales? In others, is the estimated coefficient of PRICE statistically signifigant at the 5% level? Explan.

3. Does Price effect Sale? Y/N WHY?

Sales	ADV	PRICE
3	1	8
4	2	7.5
6	3	7.25
5	4	7.25
7	5	6
6	6	6.75
5	7	6
9	8	5
10	9	4.4
9	10	5.2

Answer 1

The regression results obtained using Microsoft Excel is as follows:

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.932 0.868 0.831 0.954 10 ANOVA df F 23.114 Significance F 0.001 Regression Residual Total SS MS 42.035 21.017 6.365 0.909 48.400 Intercept ADV PRICE Coefficients Standard Error Stat P-value 17.684 6.187 2.858 0.024 0.292 0.017 0.987 -1.785 0.735 -2.430 0.045 Lower 95% Upper 95% Lower 95.0% 3.053 32.314 3.053 -0.685 0.695 -0.685 -3.523 -0.048 -3.523 Upper 95.0% 32.314 0.695 -0.048 0.005

(1) R-squared of 0.868 tells us that 86.5% of variations in sales is explained by advertisement and price jointly.

(2) Since the p-value of the price coefficient is 0.045, which is less than 0.05, we reject the null hypothesis that price does not affect sales and conclude that price coefficient is statistically significant. This can also be concluded by looking at the t value, which has a absolute value of 2.43, which is greater than the critical value of t with 2 degree of freedom at 5% level of significance. Also, the 95% confidence interval given in the output can be used to get this conclusion. The price coefficient of -1.785 lies within the confidence interval (i.e., -3.523 < -1.785 < 0.048

(3) Yes, price affects sales. In the present example, since price coefficient is statistically significant, we may conclude that price affects sales.