AP Stats Inference for Slopes

Which of the following is NOT one of the conditions that must be satisfied in order to perform inference about the slope of a least-squares regression line?

• For each value of x, the population of y-values is Normally distributed.

• The standard deviation ó of the population of y-values corresponding to a particular value of x is always the same, regardless of the specific value of x.

•  The sample size—that is, the number of paired observations (x, y)—exceeds 30

•  The data come from a random sample or a randomized experiment.

Inference about the slope β of a least-squares regression line is based on which of the following distributions?

• The t distribution with n – 1 degrees of freedom

• The standard Normal distribution

• The Chi-square distribution with n – 1 degrees of freedom

• The t distribution with n – 2 degrees of freedom

• The Normal distribution with mean µ and standard deviation ó

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 and the player’s total winnings for the previous season are recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software.

The correlation between total winnings and average number of putts per hole for these players is

• -0.285

• -0.081

• -0.007

• 0.081

• 0.285

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 and the player’s total winnings for the previous season are recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software.

Suppose that the researchers test the hypothesis H₀: β=0, H_a: β<0. The value of the t statistic for the test is

• 2.61

• 2.44

• 0.081

• -2.44

• -20.24

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 and the player’s total winnings for the previous season are recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software.

The p-value for the test is 0.0087. A correct interpretation for this result is that

• the probability that there is no linear relationship between average number of putts per hole and total winnings for these 69 players is 0.0087.

• the probability there is no linear relationship between average number of putts per hole and total winnings for all players on the PGA Tour’s world money list is 0.0087.

• if there is a linear relationship between average number of putts per hole and total winnings for the players in the sample, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of -4139198 or less is 0.0087.

• if there is no linear relationship between the number of putts per hole and total winnings for the players on the PGA Tours world money list, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of -4139198 or less is 0.0087.

• the probability of making a Type II error is 0.0087.

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 and the player’s total winnings for the previous season are recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software.

A 95% confidence interval for the slope β of the population regression line is

• 7,897,179 + 3,023,782

• 7,897,179 + 6,047,564

• -4,139,198 + 1,698,371

• -4,139,198 + 3,328,807

• -4,139,198 + 3,396,742

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 and the player’s total winnings for the previous season are recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software.

A residual plot from the least-squares regression is shown. Which of the following statements is supported by the graph?

• The residual plot contains dramatic evidence that the standard deviation of the response about the population regression line increases as the average number of putts per round increases.

• The sum of the residuals is not 0. Obviously, there is a major error present.

• Using the regression line to predict a player’s total winnings from his average number of putts almost always results in errors of less than $200,000.

• For two players, the regression line under-predicts their total winnings by more than $800,000.

• The residual plot reveals a strong positive correlation between average putts per round and prediction errors from the least-squares line for these eleven years.

To determine property taxes, Florida reappraises real estate every year, and the county appraiser's Web site lists the current "fair market value" of each piece of property. Property usually sells for somewhat more than the appraised market value. we collected data on the appraised market values x and actual selling prices y (in thousands of dollars) of a random sample of 16 condominium units in Florida. We checked that the conditions for inference about the slope of the population regression line are met. Here is part of the Minitab output from a least-squares regression analysis using these data.

What is the LSRL of the data?

• 
• 
• 
• 
• 

To determine property taxes, Florida reappraises real estate every year, and the county appraiser's Web site lists the current "fair market value" of each piece of property. Property usually sells for somewhat more than the appraised market value. we collected data on the appraised market values x and actual selling prices y (in thousands of dollars) of a random sample of 16 condominium units in Florida. We checked that the conditions for inference about the slope of the population regression line are met. Here is part of the Minitab output from a least-squares regression analysis using these data.

The slope β of the population regression line describes

• the exact increase in the selling price of an individual unit when its appraised value increases by $1000

• the average increase in the appraised value in a population of units when selling price increases by $1000 

• the average increase in selling price in a population of units when appraised value increases by $1000

• the average increase in the appraised value in the sample of units when selling price increases by $1000

• the average increase in selling price in the sample of units when the appraised value increases by $1000

To determine property taxes, Florida reappraises real estate every year, and the county appraiser's Web site lists the current "fair market value" of each piece of property. Property usually sells for somewhat more than the appraised market value. we collected data on the appraised market values x and actual selling prices y (in thousands of dollars) of a random sample of 16 condominium units in Florida. We checked that the conditions for inference about the slope of the population regression line are met. Here is part of the Minitab output from a least-squares regression analysis using these data.

Is there convincing evidence that selling price increases as appraised value increases?  To answer this question, test the hypotheses