Question

The following table compares the completion percentage and interception percentage of 5 NFL quarterbacks.

Completion Percentage	56	57	64	65	66
Interception Percentage	4.5	3	2.5	2	1.5

Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.

Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Step 3 of 6: According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable y^ is given by?

Step 4 of 6: Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.

Step 5 of 6: Find the estimated value of y when x=65. Round your answer to three decimal places.

Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

Step 1: Sum of X = 308
Sum of Y = 13.5
Mean X = 61.6
Mean Y = 2.7
Sum of squares (SS_X) = 89.2
Sum of products (SP) = -19.6

Regression Equation = ŷ = bX + a

b = SP/SS_X = -19.6/89.2 = -0.220

Step 2: a = M_Y - bM_X = 2.7 - (-0.22*61.6) = 16.235

Step 3: This value is same as slope so answer is -0.220

Step 4:

So answer is False

Step 5: Regression equation is

ŷ = -0.220X + 16.235

For x=65, y=-0.220*65 + 16.235=1.935

Step 6. X Values
∑ = 308
Mean = 61.6
∑(X - M_x)² = SS_x = 89.2

Y Values
∑ = 13.5
Mean = 2.7
∑(Y - M_y)² = SS_y = 5.3

X and Y Combined
N = 5
∑(X - M_x)(Y - M_y) = -19.6

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = -19.6 / √((89.2)(5.3)) = -0.901

So coefficient of determination is r^2=0.812