Evaluating the Fit of a Model â Calculate and interpret an r-squared ...
Evaluating the Fit of a Model – Calculate and interpret an r-squared value Check for Understanding In a study of the growth of sparrows, data were gathered on the wing length (cm) and age (days) of 13 sparrows. A regression was performed with the following results:
What is the value of the coefficient of determination? What does the coefficient of determination tell you about the relationship?
A study found the correlation between the heights of men and the heights of their biological sons to be r = 0.71. What is the approximate value of r2 and what does this value tell you?
A high school counselor at a large public high school is interested in developing a model to predict SAT math scores. He takes a random sample of 50 seniors at the school who took the SAT exam and recorded SAT math score, the number of math courses completed at the high school and the number of science courses completed at the high school for each of the students in the sample. Computer output resulting from fitting a linear regression model is given below:
Interpret the value of r2 in context.
Answers 1. The value of r-squared is 97.3%. This suggests that 97.3% of the variability in wing length (in cm) can be explained by the linear relationship with age (in days) of sparrows 2. The approximate value is 0.50, and it represents the proportion of the variability in sons’ heights that can be explained by the approximate linear relationship between fathers’ heights and sons’ heights. 3. From the computer output, r2 is 0.784. This means that about 78% of the variability in SAT math scores can be attributed to an approximate linear relationship between the number of math courses completed and SAT score.
What is the value of the coefficient of determination? What does the coefficient of determination tell you about the relationship?
A study found the correlation between the heights of men and the heights of their biological sons to be r = 0.71. What is the approximate value of r2 and what does this value tell you?
A high school counselor at a large public high school is interested in developing a model to predict SAT math scores. He takes a random sample of 50 seniors at the school who took the SAT exam and recorded SAT math score, the number of math courses completed at the high school and the number of science courses completed at the high school for each of the students in the sample. Computer output resulting from fitting a linear regression model is given below:
Interpret the value of r2 in context.
Answers 1. The value of r-squared is 97.3%. This suggests that 97.3% of the variability in wing length (in cm) can be explained by the linear relationship with age (in days) of sparrows 2. The approximate value is 0.50, and it represents the proportion of the variability in sons’ heights that can be explained by the approximate linear relationship between fathers’ heights and sons’ heights. 3. From the computer output, r2 is 0.784. This means that about 78% of the variability in SAT math scores can be attributed to an approximate linear relationship between the number of math courses completed and SAT score.
