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

a)The F critical value for a right-tailed test, for a significance level of α=0.05 is

Critical value of F​=4.543 < F stat

b)Coefficient of determination r^2 = SSR/SST = 372.707/502.941 = 0.741

c)Explained variance is 74% and unexplained variance is 26%

correlation coefficient = r = 0.861

d) ŷ = b₀ + b₁x

ŷ = 45.623 + 0.107 * x

Rating = 45.623 + 0.107 * Price

e)

t stat for β₁ = 6.552 and p value = 0 < 0.05

there is a strong relation between Rating and price

t = β₁ / Sqrt(SSE/((n-2)(SS_xx)))

t test for β₀ = 12.569 and P value = 0 < 0.05

there is a strong relation between Rating and price

t = β₀ / Sqrt(SSE/((n-2)(SS_yy)))

(t value and p value given in the above table)