Exercises T12.4–T12.8 refer to the following setting. An old saying in golf is “You drive for show and you putt for dough.” The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour’s world money list are examined. The average number of putts per hole (fewer is better) and the player’s total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for
inference about the slope are met. Here is computer output from the regression analysis:

T12.8 Which of the following would make the calculation in Exercise T12.7 invalid?

a. If the scatterplot of the sample data wasn’t perfectly linear.

b. If the distribution of earnings has an outlier.

c. If the distribution of earnings wasn’t approximately Normal.

d. If the earnings for golfers with small putting averages was much more variable than the earnings for golfers with large putting averages.

e. If the standard deviation of earnings is much larger than the standard deviation of putting average.

To determine the option that make the calculation in Exercise $T12.7$invalid.

For shooting low scores and hence winning money, it is assumed that good putting is more significant than long driving.
A random sample of players is picked for analysis to see if this is the fact.
They assumed that the slope inference conditions were met, and that the data was calculated using the computer output provided in the question.
Assume the researcher is putting the theory to the test.
The test statistic's P-value is $0.0087$.
Linear, Normal, Equal standard deviation, and Random are the requirements for regression inference. As a result, after considering our alternatives,
Because the linear requirement requires that the sample data be approximately linear, the calculation will still be correct in option (a).
Because there is no restriction on the distribution of the $x$-variable or $y$-variable in option (b), the calculation will still be valid.
Because there is no restriction on the distribution of the $x$-variable or $y$-variable in option (c), the calculation will still be valid.
The calculation will no longer be valid in option (d), as the vertical spread in the scatterplot will no longer be constant, violating the equal standard deviations assumption.
Because the equal standard deviation criteria applies to the residuals, option (e) will keep the calculation valid.
As a result, option (d) is the correct answer.