AP Stats Unit 3 Chapter 4

To determine property taxes, Florida reappraises real estate every year, and the county appraiser's website 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 the 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. Which of the following is the best interpretation for the value 0.1126 in the computer output?

• For each increase of $1000 in appraised value, the average selling price increases by about 0.1126.

• When using this model to predict selling price, the predictions will typically be off by about 0.1126.

• 11.26% of the variation in selling price is accounted for by the linear relationship between selling price and appraised value.

• There is a weak, positive linear relationship between selling price and appraised value.

• In repeated samples of size 16, the sample slope will typically vary from the population slope by about 0.1126.

To determine property taxes, Florida reappraises real estate every year, and the county appraiser's website 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 the 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. A 95% confidence interval for the population slope beta is

To determine property taxes, Florida reappraises real estate every year, and the county appraiser's website 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 the 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. Which of the following would have resulted in a violation of the conditions for inference?

• If the entire sample was selected from one neighborhood

• If the sample size was cut in half

• If the scatterplot x= appraised value and y= selling price did not show a perfect linear relationship

• If the histogram of selling prices had an outlier

• If the standard deviation of appraised values was different from the standard deviation of selling prices

A roadrunner is a desert bird that tends to run instead of fly. While running, the roadrunner uses its tail as a balance. A sample of 10 roadrunners was taken, and the birds’ total length, in centimeters (cm), and tail length, in cm, were recorded. The output shown in the table is from a least-squares regression to predict tail length given total length. Suppose a roadrunner has a total length of 59.0 cm and tail length of 31.1 cm. Based on the residual, does the regression model overestimate or underestimate the tail length of the roadrunner?

• Underestimate, because the residual is positive.

• Underestimate, because the residual is negative.

• Overestimate, because the residual is positive.

• Overestimate, because the residual is negative.

• Neither, because the residual is 0.

The equation of the least squares regression line for a set of data is y=0.68+1.21x. What is the residual for the point (3, 4)?

• -0.31

• -0.68

• -1.52

• -3.63

• -4.31

Meg has a set of bivariate numerical data with a correlation coefficient of r=0.83. Elise has a data set with a correlation coefficient of r=-0.83. What can you conclude about the two sets of data?

• The scatterplots for these two data sets both display a strong linear pattern.

• In Meg’s data, 83% of the data points are closely related.

• In Elise’s data, 83% of the variability in y can be explained by the linear association with x.

• Meg’s data is more linear than Elise’s data.

• Nothing can be concluded about the two data sets without looking scatterplots of the data.

Given the following Minitab output, which of the following is false?

• 80% of the variability in y is explained by the linear relationship with x.

• Since r=0.898, the linear relationship between x and y is strong, positive, and linear.

• As x increases by one unit, y decreases, on average, by 1.6914 units.

• The intercept of the least squares regression line is -0.868.

• The equation of the least squares regression line is y=-0.868-1.6914x.

There is a linear relationship between the amount of fat in a sandwich and the amount of calories in a sandwich. A least squares line was fit using some data collected by nutritionists, resulting in the equation y=217.3+35.2xwhere x is fat grams and y is caloric content. What is the estimated caloric content of a sandwich with 8 grams of fat?

• 35.2 calories

• 217.3 calories

• 281.6 calories

• 498.9 calories

• 1738.4 calories

Two variables are exponentially related. The least squares regression lines for transformed data is found to be ln y=-0.041+0.0035x. What is the predicted value for y when x=16.83?

• 2.49

• 1.018

• 12.98

• 16.74

• 54.15

A scatterplot of x = Super Bowl and y = cost of a 30-second advertisement on the Super Bowl broadcast (in dollars) shows a strong, positive, nonlinear association. A scatterplot of ln(cost) versus Super Bowl number is roughly linear. The least squares regression line for this association is predicted ln(cost)=10.97+0.0971(Super Bowl number). Predict the cost of a 30-second advertisement for Super Bowl 40.

• $3

• $15

• $58,153

• $83,132

• $2,824,947