Linear Regression

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 residual plots from five different least squares regression lines are shown below. Which of the plots shows the strongest evidence that its regression line is an appropriate model for the data and is consistent with the assumptions required for inference for regression?

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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

The computer output below shows the result of a linear regression analysis for predicting the concentration of zinc, in parts per million (ppm), from the concentration of lead, in ppm, found in fish from a certain river. Which of the following statements is a correct interpretation of the value 19.0 in the output?

• On average there is a predicted increase of 19.0 ppm in concentration of lead for every increase of 1 ppm in concentration of zinc found in the fish.

• On average there is a predicted increase of 19.0 ppm in concentration of zinc for every increase of 1 ppm in concentration of lead found in the fish.

• The predicted concentration of zinc is 19.0 ppm in fish with no concentration of lead.

• The predicted concentration of lead is 19.0 ppm in fish with no concentration of zinc.

• Approximately 19% of the variability in the zinc concentration is predicted by its linear relationship with lead concentration.

Which of the following pairs of variables would be expected to have a negative association?

• GPA and height

• Number of chores and weekly allowance

• Number of hours spent studying and test grade

• Number of miles driven and amount of gas remaining in gas tank

• Age and IQ

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

Which of the following scatter plots could have created the residual plot below?

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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