Question

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

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

 Completion Percentage Interception Percentage 56 57 64 65 66 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. Step 1: Sum of X = 308
Sum of Y = 13.5
Mean X = 61.6
Mean Y = 2.7
Sum of squares (SSX) = 89.2
Sum of products (SP) = -19.6

Regression Equation = ŷ = bX + a

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

Step 2: a = MY - bMX = 2.7 - (-0.22*61.6) = 16.235

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

Step 4: 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 - Mx)2 = SSx = 89.2

Y Values
∑ = 13.5
Mean = 2.7
∑(Y - My)2 = SSy = 5.3

X and Y Combined
N = 5
∑(X - Mx)(Y - My) = -19.6

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -19.6 / √((89.2)(5.3)) = -0.901

So coefficient of determination is r^2=0.812

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