Question

1. The following output was obtained from a regression analysis of the dependent variable Rating and an independent variable Price. (10 points)

ANOVA
	df	SS	MS	F
Regression	1	372.707	372.707	42.927
Residual	15	130.234	8.682
Total	16	502.941
	Coefficients	Standard Error	t Stat	P-value
Intercept	45.623	3.630	12.569	0.000
Price	0.107	0.016	6.552	0.000

1. Use the critical value approach to perform an F test for the significance of the linear relationship between Rating and Price at the 0.05 level of significance.
2. Calculate the coefficient of determination.
3. What percentage of the variability of Rating can be explained by its linear relationship with Price? What is the sample correlation coefficient?
4. What is the estimated regression equation?
5. Use the p-value approach to perform a t test for the significance of the linear relationship between Price and Rating at the 0.05 level of significance.

Answer 1

Solution:
Part a) Use the critical value approach to perform an F test for the significance of the linear relationship between Rating and Price at the 0.05 level of significance

df_N= 1

df_D = 15

Look in F table for df_N= 1 and df_D = 15

F critical value= 4.54

From ANOVA table , F_calc = 42.927

Since F_calc = 42.927 > F critical value= 4.54, we reject null hypothesis H0 and conclude that: there is significant linear relationship between Rating and Price at the 0.05 level of significance.

Part b) Calculate the coefficient of determination.

From ANOVA table,

SSR = 372.707

SST = 502.941

Thus

Part c) What percentage of the variability of Rating can be explained by its linear relationship with Price?

Thus 74.11 % of the variability of Rating can be explained by its linear relationship with Price.

What is the sample correlation coefficient?

the sample correlation coefficient r = 0.8608

Part d) What is the estimated regression equation?

Rating = 45.623 + 0.107 X Price

Part e) Use the p-value approach to perform a t test for the significance of the linear relationship between Price and Rating at the 0.05 level of significance.

From given table, P-value for slope of regression equation ( coefficient of Price) is = 0.000

Since this P-value = 0.000 < 0.05 level of significance, we conclude that : there is significant linear relationship between Price and Rating at the 0.05 level of significance.