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 55.2 57.6 58.2 62.9 64.9

Interception Percentage 4.3 3.6 1.6 1.1 1 Table

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:Determine the value of the dependent variable yˆy^ at x=0x=0.

Answer 1

The statistical software output for this problem is:

Simple linear regression results: Dependent Variable: Interception Independent Variable: Completion Interception = 22.142529 - 0.3317023 Completion Sample size: 5 R (correlation coefficient) = -0.87094972 R-sq = 0.75855341 Estimate of error standard deviation: 0.86552197

Hence,

Step - 1: Slope = -0.332

Step - 2: y-intercept = 22.143

Step - 3: Value of dependent variable = 22.143