Q: 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?

$$\text{Distance} = -55.797 + 3.166 \times \text{Speed}$$

Q: If a golfer swings with a club-head speed of 100 mph, what is the predicted distance the ball will travel according to the regression equation?

$$\text{Distance} = -55.797 + 3.166 \times 100 = 260.803$$

Q: If the observed distance for a club-head speed of 100 mph is 265 yards, what is the residual for this observation?

$$\text{Residual} = 265 - 260.803 = 4.197$$

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

$$	ext{Distance} = -55.797 + 3.166 	imes 	ext{Speed}$$

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 3.166 yards, on average.

Question 3

According to the regression output, what is the interpretation of the y-intercept ($$-55.797) in $$this context?

Accepted Answer

It represents the predicted distance when club-head speed is 0, but this value is not meaningful in this context.

Question 4

If a golfer swings with a club-head speed of 100 mph, what is the predicted distance the ball will travel according to the regression equation?

Accepted Answer

$$	ext{Distance} = -55.797 + 3.166 	imes 100 = 260.803$$

Question 5

Which of the following statements is supported by the regression output regarding the statistical significance of the slope?

Accepted Answer

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

Question 6

What does the $$R^2$$ value of 0.8811 (from the StatCrunch output) indicate about the regression model?

Accepted Answer

88.11% of the variation in distance is explained by club-head speed.

Question 7

If the observed distance for a club-head speed of 100 mph is 265 yards, what is the residual for this observation?

Accepted Answer

$$	ext{Residual} = 265 - 260.803 = 4.197$$

Question 8

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

Accepted Answer

Excel output only

Question 9

Suppose the p-value for the intercept is 0.295. What does this imply about the statistical significance of the intercept?

Accepted Answer

The intercept is not statistically significant at the 0.05 significance level.

Question 10

Which of the following is a correct interpretation of the regression coefficient for Club-Head Speed based on the outputs?

Accepted Answer

For each 1 mph increase in club-head speed, the expected distance increases by approximately 3.166 yards.

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

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