Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained. = 12 + 1.8x

N = 17
SSR = 225
SSE = 75
Sb₁ = .2683
The t statistic for testing the significance of the slope is

Question

Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained.

= 12 + 1.8x

N = 17
SSR = 225
SSE = 75
Sb₁ = .2683
The t statistic for testing the significance of the slope is

Quizplus · Accepted Answer

The t statistic for testing the significance of the slope can be calculated using the formula: t = b / (SEb) where b is the estimated slope coefficient, and SEb is the standard error of the slope coefficient. From the given information, b = 1.8 and Sb₁ = .2683. Therefore, SEb = .2683 / sqrt(17) ≈ .065. Substituting these values into the formula for t, we get: t = 1.8 / .065 ≈ 27.69 This t statistic is much larger than the critical t-value for a two-tailed test with 15 degrees of freedom and a significance level of .05, which is approximately 2.13. Therefore, we can reject the null hypothesis that the slope is equal to zero and conclude that there is a significant linear relationship between advertising and sales. The correct choice is C.

Regression Analysis Was Applied Between Sales Data (Y in $1000s)