Exam 30: Multiple Regression Wisdom

A real estate agent wishes to predict the selling price of a home based on several variables.One categorical variable of interest is the quality of the home - low,medium,or high.If the real estate agent wished to include "quality" in a regression model,how many indicator variables would he/she need to use in the model?

Here are plots for Studentized residuals against Chest. Here is the same regression with the two data points with residuals above 2 removed: Dependent variable is: Weight 30 total bears of which 2 are missing R-squared = 93.8% R-squared (adjusted)= 93.0% s = 7.22 with 28 - 4 = 24 degrees of freedom Compare the regression with the previous one.In particular,which model is likely to make the best prediction of weight? Which seems to fit the data better?

Here are plots of data for Studentized residuals against Length. Here is the same regression with all of the points at 70 removed. Dependent variable is: Weight 30 total bears of which 10 are missing R-squared = 97.8% R-squared (adjusted)= 97.3% s = 2.96 with 20 - 4 = 16 degrees of freedom Compare the regression with the previous one.In particular,which model is likely to make the best prediction of weight? Which seems to fit the data better?

An actuary wishes to predict the life expectancy of a person based on several variables.One categorical variable of interest is their relationship status - single,married,divorced,widowed,or common-law.If the actuary wished to include "relationship status" in a regression model,how many indicator variables would he/she need to use in the model?

A math professor is trying to determine if her students' math grades are consistent with their grades in three other courses.She has 30 students who are all taking Math,Science,English,and an Elective course.She assigns scores of 4,3,2,and 1 for each grade of A,B,C,and D,respectively.Here's a regression model to predict the math grade based on the other courses: Dependent variable is: Math R-squared = 84.4% R-squared (adjusted)= 82.6% s = 0.3789 with 30 - 4 = 26 degrees of freedom -Here is a histogram of leverages for this regression: Without doing any calculating,how would you expect the coefficient and t-statistic of English to change if we were to omit the 6 highest leverage points?

Here are plots of data for Studentized residuals against Chest. Interpret this plot of the residuals.

The manager of a human resources department wishes to predict the salary of an employee based on years of experience,x,and gender,g.(g = 1 for a male employee and 0 for a female employee).A random sample of 50 employees results in the following least-squares regression equation: = 40,000 + 2,500 x + 1,500 g.What is the least-squares regression line for predicting the salary of male employees?

The manager of a human resources department wishes to predict the salary of an employee based on years of experience,x,and gender,g.(g = 1 for a male employee and 0 for a female employee).A random sample of 50 employees results in the following least-squares regression equation: = 40,000 + 2,500 x + 1,500 g +1,000 xg.What is the least-squares regression line for predicting the salary of male employees?

A histogram of the externally Studentized residuals looks like this: Comment on the distribution of the Studentized Residuals.

A company hired 25 employees for various positions.After the candidates were chosen,they wanted to see what the relationship of starting salary was based on years of experience and education level.They assign a 0,1,2,or 3 for high school diploma,bachelor's degree,master's degree,or a doctorate,respectively.The regression model looks like this: Dependent variable is: Salary R-squared = 69.6% R-squared (adjusted)= 66.9% s = 7889 with 25 - 3 = 22 degrees of freedom -Here are histograms of the leverage and Studentized residuals for the regression model: Comment on what these diagnostic displays indicate.

The manager of a human resources department wishes to predict the salary of an employee based on years of experience,x,and gender,g.(g = 1 for a male employee and 0 for a female employee).A random sample of 50 employees results in the following least-squares regression equation: = 40,000 + 2,500 x + 1,500 g +1,000 xg.What is the least-squares regression line for predicting the salary of female employees?

A math professor is trying to determine if her students' math grades are consistent with their grades in three other courses.She has 30 students who are all taking Math,Science,English,and an Elective course.She assigns scores of 4,3,2,and 1 for each grade of A,B,C,and D,respectively.Here's a regression model to predict the math grade based on the other courses: Dependent variable is: Math R-squared = 84.4% R-squared (adjusted)= 82.6% s = 0.3789 with 30 - 4 = 26 degrees of freedom -How would you interpret the coefficient of Science in the multiple regression?

Here are plots of data for Studentized residuals against Length. Interpret this plot of the residuals.

How would you interpret the coefficient of sex in this model?

The manager of a human resources department wishes to predict the salary of an employee based on years of experience,x,and gender,g.(g = 1 for a male employee and 0 for a female employee).A random sample of 50 employees results in the following least-squares regression equation: = 40,000 + 2,500 x + 1,500 g +1,000 xg.Interpret the value of the coefficient of the interaction term xg.

The manager of a human resources department wishes to predict the salary of an employee based on years of experience,x,and gender,g.(g = 1 for a male employee and 0 for a female employee).A random sample of 50 employees results in the following least-squares regression equation: = 40,000 + 2,500 x + 1,500 g +1,000 xg.Interpret the value of the coefficient of gender (g).

What is the purpose of an indicator variable in a regression model?

The manager of a human resources department wishes to predict the salary of an employee based on years of experience,x,and gender,g.(g = 1 for a male employee and 0 for a female employee).A random sample of 50 employees results in the following least-squares regression equation: = 40,000 + 2,500 x + 1,500 g.What is the least-squares regression line for predicting the salary of female employees?

A math professor is trying to determine if her students' math grades are consistent with their grades in three other courses.She has 30 students who are all taking Math,Science,English,and an Elective course.She assigns scores of 4,3,2,and 1 for each grade of A,B,C,and D,respectively.Here's a regression model to predict the math grade based on the other courses: Dependent variable is: Math R-squared = 84.4% R-squared (adjusted)= 82.6% s = 0.3789 with 30 - 4 = 26 degrees of freedom -Here is the scatterplot of externally Studentized residuals against predicted values: Comment on what this diagnostic display indicates.

The manager of a human resources department wishes to predict the salary of an employee based on years of experience,x,and gender,g.(g = 1 for a male employee and 0 for a female employee).A random sample of 50 employees results in the following least-squares regression equation: = 40,000 + 2,500 x + 1,500 g +1,000 xg.Predict the salary for a male employee with 15 years of experience.