Question

The table below gives the completion percentage and interception percentage for five randomly selected NFL quarterbacks. Based on this data, consider the equation of the regression line, yˆ=b0+b1x, for using the completion percentage to predict the interception percentage for an NFL quarterback. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Completion Percentage 57 59 62 63 64
Interception Percentage 5 3.5 3 2.5 1.5
Table

6 steps

Answer 1

The regression equation is y = -0.42647x + 29.11471 and the correlation coefficient is -0.9607

How to determine the regression equation?

The table of values is given as:

Completion Percentage 57 59 62 63 64

Interception Percentage 5 3.5 3 2.5 1.5

Next, we enter the above values in a graphing calculator.

From the graphing calculator, we have the following summary:

• Sum of X = 305
• Sum of Y = 15.5
• Mean X = 61
• Mean Y = 3.1
• Sum of squares (SSX) = 34
• Sum of products (SP) = -14.5
• r = -0.9607

Regression Equation = ŷ = bX + a

b = SP/SSX = -14.5/34 = -0.42647

a = MY - bMX = 3.1 - (-0.43*61) = 29.11471

So, the regression equation is

y = -0.42647x + 29.11471

And the correlation coefficient is -0.9607

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