Linear Regression Analysis and Correlation

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 zinc concentration is predicted by its linear relationship with lead concentration.

• 3.3 F

• 16.5 F

• 25.2 F

• 28.5 f

• 41.7 F

The height h and collar size c, both in centimeters, measured from a sample of boys were used to create the regression line c = -94 + 0.9h. The line is used to predict collar size from height, both in centimeters, for boys' shirt collars.

Which of the following has no logical interpretation in context?

• The predicted collar size of a boy with height 140 cm

• The h values in the sample

• The c values in the sample

• The slope of the regression line

• The c-intercept of the regression line

• y = -5 + 3x

• y = 3x

• y = 5+2.5x

• y = 8.5+.3x

• y = 10+.4x

A field researcher who studies lions conjectured that the more time a cub spends playing, the sooner the cub will begin to hunt. Observational data wee collected from 20 lion cubs. The researcher recorded how long they spent playing and the age when they began hunting. Because male and female lions have different hunting behaviors, the researcher recorded the data for males and females separately. The two scatterplots show the data for the 10 female lions and the 10 male lions.

For which gender does there appear to be evidence that the more time a lion cub spends playing, the sooner the cub is likely to begin hunting?

• For female cubs only

• For male cubs only

• For both male cubs and female cubs, with equal evidence

• For both male cubs and female cubs, with more evidence for female cubs than for male cubs

• For neither male cubs nor female cubs

Suppose a certain scale is not calibrated correctly, and as a result, the mass of any object is displayed as 0.75 kilogram less than its actual mass. What is the correlation between the actual masses of a set of objects and the respective masses of the same set of objects displayed by the scale?

• -1

• -0.75

• 0

• 0.75

• 1

For a random sample of 20 professional athletes, there is a strong, linear relationship between the number of hours they exercise per week and their resting heart rate. For the athletes in the sample, those who exercise more hours per week tend to have lower resting heart rates than those who exercise less. Which of the following is a reasonable value for the correlation between the number of hours athletes exercise per week and their resting heart rate?

• 0.71

• 0.00

• -0.14

• -0.87

• -1.00

An experiment was conducted to investigate the relationship between the does of a pain medication and the number of hours of pain relief. Twenty individuals with chronic pain were randomly assigned to one of five doses - 0.0, 0.5, 1.0, 1.5, 2.0 - in milligrams (mg) of medication. The results are shown in the scatterplot below.

The data were used to fit a least-squares regression line to predict the number of hours of pain relief for a given dose. Which of the following would be revealed by a plot of the residuals of the regression versus the dose?

• The sum of the residuals is less than 0.

• The sum of the residuals is greater than 0.

• There are outliers associated with the lower doses.

• The variation in the hours of pain relief is not the same across the doses.

• There is a positive linear relationship between the residuals and the dose.

The height and age of each child in a random sample of children was recorded. The value of the correlation coefficient between height and age for the children in the sample was 0.8. Based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?

• On average, the height of a child is 80% of the age of the child.

• The least-squares regression line of height versus age will have a slope of 0.8.

• The proportion of the variation in height that is explained by a regression on age is 0.64.

• The least-squares regression line will correctly predict height based on age 80% of the time.

• The least-squares regression line will correctly predict height based on age 64% of the time.

Data were collected on the fiber diameter and the fleece weight of wool taken from a sample of 20 sheep. The data are shown in the following graphs. Graph 1 is a scatterplot of fleece weight versus fiber diameter with the respective least-squares regression line shown. Graph 2 is the associated plot of the residuals versus the predicted values.

One point is circled on graph 1. Five points labeled A, B, C, D and E are identified on graph 2. Which point on graph 2 represents the residual for the circled point on graph 1?

• A

• B

• C

• D

• E