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+b1xy^=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	56	57	60	62	64
Interception Percentage	5	4	3.5	3	2

Table

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Find the estimated slope. Round your answer to three decimal places.

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Answer 1

We have given data bsed on completion percentage and interception percentage for randomly selected NFL quarterback. The completion percentage is represented by x and interception percentage is represented by y which is given below

Inorder to estimate y, let us consider model as

For minimizing the residual sum of error, we differentiate it with respect to the two paramter and we equate it to 0.This gives two normal equation which is given below

Therefore the paramter and slope of the equation is

Now, we try to obtain to obtain the slope of the equation so consider the table below

Therefore the slope and intercept is

Therefore the regression equation is