Question 1

Based on the regression outputs shown in the image, what is the equation of the least-squares regression line for predicting Distance from Club-Head Speed?

Accepted Answer

$$y = 3.166x - 55.796$$

Question 2

Interpret the slope of the regression line as shown in the outputs. What does the value 3.166 mean in this context?

Accepted Answer

For each additional mile per hour in club-head speed, the distance the golf ball travels increases by approximately 3.166 yards, on average.

Question 3

According to the regression output, is the y-intercept meaningful in this context? Why or why not?

Accepted Answer

No, because a club-head speed of 0 mph is not a reasonable value in this context.

Question 4

What is the value of the coefficient of determination $$R^2 as $$shown in the StatCrunch output, and what does it represent?

Accepted Answer

$$R^2 = 0.881$; it means that 88.1\% of the variation in distance is explained by club-head speed.

Question 5

Using the regression equation $$\hat{y} = -55.7966 + 3.166x$$, what is the predicted distance for a club-head speed of 100 mph?

Accepted Answer

$$\hat{y} = 260.8$$

Question 6

If the observed distance for a club-head speed of 100 mph is 265 yards, what is the residual for this observation using the regression equation $$\hat{y} = -55.7966 + 3.166x$$?

Accepted Answer

$$265 - 260.8 = 4.2$$

Question 7

Which of the following best describes the statistical significance of the slope coefficient for Club-Head Speed, based on the Excel output?

Accepted Answer

The slope is statistically significant because the p-value is much less than 0.05.

Question 8

Suppose a new observation with a club-head speed of 120 mph and a distance of 305 yards is added to the data. Based on the concepts of influential observations, what is likely to happen?

Accepted Answer

The regression line's slope and y-intercept may change substantially, indicating the new point is influential.

Question 9

If the residual plot for this regression shows a U-shaped pattern, what does this indicate about the appropriateness of the linear model?

Accepted Answer

The linear model is not appropriate; a nonlinear model may be better.

Question 10

Which output(s) in the image provide(s) the standard error of the regression coefficients?

Accepted Answer

The Excel output only.

Describing the Relation Between Two Variables: Scatter Diagrams, Correlation, and Regression

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