WorksheetsLinear Regression and Residuals
Total questions: 7
Worksheet time: 11mins
How do you calculate residuals in least squares regression?
By adding the predicted values to the actual values of the response variable.
By multiplying the predicted values with the actual values of the response variable.
By dividing the predicted values by the actual values of the response variable.
By subtracting the predicted values from the actual values of the response variable.
How do you interpret the coefficient of determination in least squares regression?
The coefficient of determination represents the correlation between the explanatory and response variables.
The coefficient of determination represents the proportion of the variance in the response variable that can be explained by the explanatory variable(s).
The coefficient of determination represents the average of the explanatory and response variables.
The coefficient of determination represents the proportion of the variance in the explanatory variable that can be explained by the response variable(s).
The National Directory of Magazines tracks the number of magazines published in the United States each year. An analysis of data from 1988 to 2007 gives the following computer output. The dates were recorded as years since 1988. Thus, the year 1988 was recorded as year 0. A residual plot (not shown) showed no pattern.
(b) Interpret the slope in the context of this situation.
As the the year increases by 1, the number of magazines sold tends to increase by 325.39.
Our model predicts on average that as the the year decreases by 1, the number of magazines sold tends to increase by 325.39.
Our model predicts on average that as the the year increases by 1, the number of magazines sold tends to increase by 325.39.
The number of magazines sold increases by 325.39 as the year increases by 1.
The number of magazines sold decreases by 325.39 as the year increases by 1.
The heights (in inches) and weights (in pounds) of six male Labrador Retrievers were measured. The height of a dog is measured at the shoulder. A linear regression was done, and the residual plot and computer output are given to the left.
Dakota, a male Labrador, was one of the dogs measured for this study. His height is 23.5 inches. What. is Dakota's actual weight?
Not enough information is provided.
1.6 lbs
73.42
75.02
Suppose the correlation between two variables is r = 0.23. What will the new correlation be if 0.14 is added to all values of the x-variable, every value of the y-variable is doubled, and the two variables are interchanged?
0.23
0.37
0.74
-0.23
-0.74
In a random sample of older patients at a large medical practice, the age of a patient and a measure of that patient's hearing loss were recorded. The correlation between age and hearing loss of the patients in the sample was found to be 0.7. Which one of the following would be a correct statement if the age of a patient were used to predict the amount of hearing loss for a patient?
49% of the time the LSRL accurately predicts hearing loss.
49% of the variation in hearing loss can be explained by the variation in the age of a patient.
About 70% of a person's hearing loss can be explained by age according to the LSRL relating hearing loss and age.
About 70% of the time, age will correctly predict the amount of hearing loss.
The LSRL relating hearing loss to age will have a slope of approximately 0.7.
Data was collected on two variables x and y and an LSRL was fitted to the data. The resulting equation is y-hat = -2.29 + 1.70x. What is the residual for point (5,6)?
-2.91
-0.21
0.21
6.21
7.91
