Question

# The following output was obtained from a regression analysis of the dependent variable Rating and an...

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.

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)(SSxx)))

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)(SSyy)))

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