Question

The following table compares the completion percentage and interception percentage of 5 NFL quarterbacks Completion Percentage 58 61 61 61 65 Interception Percentage 3.8 3.7 1.5 13 1.1 Table Copy Data Step 1 of 5: Caiculate the sum of sqlared errors issE), Use the values bo # 25. 1810 and bi to three decimal places -0.3742 for the calculations. Round your answer Answer How to Ener)2 Points Keypad Tables

Answer 1

x = 58 61 61 61 65

y = 3.8 3.7 1.5 1.3 1.1

Step 1:

The regression equation is given as,

$\hat{y}$ = 25.1810 - 0.3742 x

For given values of x,

$\hat{y}$ = 3.4774 2.3548 2.3548 2.3548 0.8580

SSE = $\sum (y - \hat{y})^2$

= (3.8 - 3.4774)² + (3.7 - 2.3548)² + (1.5 - 2.3548)² + (1.3 - 2.3548)² + (1.1 - 0.8580)²

= 3.815

Step 2:

s² = SSE / (n-2) = 3.815 / (5-2) = 1.272

Step 3:

$\sum x = 306$

$\sum x^2 = 18752$

$S_{xx} = \sum x^2 - (\sum x)^2/n = 18752 - 306^2/5 = 24.8$

s²_b1 = s² / Sxx = 1.272 / 24.8 = 0.051

Step 4:

Degree of freedom = n-2 = 5-2 = 3

Critical value of t at 90% confidence interval and df = 3 is  2.35

Lower endpoint = -0.3742 - 2.35 * $\sqrt{0.051}$ = -0.905

Upper endpoint = -0.3742 + 2.35 * $\sqrt{0.051}$ = 0.157

Step 5:

Critical value of t at 80% confidence interval and df = 3 is  1.64

Lower endpoint = -0.3742 - 1.64 * $\sqrt{0.051}$ = -0.745

Upper endpoint = -0.3742 + 1.64 * $\sqrt{0.051}$ = -0.004