Exam 14: Multiple Regression

Consider the following partial computer output for a multiple regression model. Analysis of Variance What is the total sum of squares?

The graph of the prediction equation obtained from the model is a(n)

The manufacturer of a light fixture believes that the dollars spent on advertising,the price of the fixture and the number of retail stores selling the fixture in a particular month,influence the light fixture sales.The manufacturer randomly selects 10 months and collects the following data: The sales are in thousands of units per month,the advertising is given in hundreds of dollars per month,and the price is the unit retail price for the particular month.Using MINITAB the following computer output is obtained. The regression equation is Sales = 31.0 + 0.820 Advertising - 0.325 Price + 1.84 Stores S = 5.465 R - Sq = 96.7% R - Sq(adj)= 95.0% Analysis of Variance Based on the multiple regression model given above,the point estimate of the monthly light fixture sales corresponding to second sample data is 49.82 or 49,820 units.This point estimate is calculated based on the assumption that the company spends $4000 on advertising,the price of the fixture is $60 and the fixture is being sold at 3 retail stores.Additional information related to this point estimate is given below. Determine the 95% confidence interval for this point estimate and interpret its meaning.

Consider the following partial computer output for a multiple regression model. Calculate R².

An investigator hired by a client suing for sex discrimination has developed a multiple regression model for employee salaries for the company in question.In this multiple regression model,the salaries are in thousands of dollars.For example,a data entry of 35 for the dependent variable indicates a salary of $35,000.The indicator (dummy)variable for gender is coded as X₁ = 0 if male and X₁ = 1 if female.The computer output of this multiple regression model shows that the coefficient for this variable (X₁)is - 4.2.The t test showed that X₁ was significant at $\alpha$ = 0.1.This result implies that for male and female workers of the company,

A member of the state legislature has expressed concern about the differences in the mathematics test scores of high school freshmen across the state.She asks her research assistant to conduct a study to investigate what factors could account for the differences.The research assistant looked at a random sample of school districts across the state and used the factors of percentage of mathematics teachers in each district with a degree in mathematics,the average age of mathematics teachers and the average salary of mathematics teachers s = 7.62090 Analysis of Variance Determine the 90% interval for $\beta$ ₂ and interpret its meaning

A member of the state legislature has expressed concern about the differences in the mathematics test scores of high school freshmen across the state.She asks her research assistant to conduct a study to investigate what factors could account for the differences.The research assistant looked at a random sample of school districts across the state and used the factors of percentage of mathematics teachers in each district with a degree in mathematics,the average age of mathematics teachers and the average salary of mathematics teachers s = 7.62090 Analysis of Variance Test the overall usefulness of the model at $\alpha$ = .01.Calculate F and make your decision.

The range of feasible values for the multiple coefficient of determination is from:

_____ variation is the sum of explained variation plus the sum of unexplained variation.

R² is defined as:

In multiple regression analysis,the mean square regression divided by mean square error yields the:

Below is a partial multiple regression ANOVA table. Calculate the proportion of the variation explained by the multiple regression model.

A member of the state legislature has expressed concern about the differences in the mathematics test scores of high school freshmen across the state.She asks her research assistant to conduct a study to investigate what factors could account for the differences.The research assistant looked at a random sample of school districts across the state and used the factors of percentage of mathematics teachers in each district with a degree in mathematics,the average age of mathematics teachers and the average salary of mathematics teachers s = 7.62090 Analysis of Variance What is the explained variation?

The manufacturer of a light fixture believes that the dollars spent on advertising,the price of the fixture,and the number of retail stores selling the fixture in a particular month,influence the light fixture sales.The manufacturer randomly selects 10 months and collects the following data: The sales are in thousands of units per month,the advertising is given in hundreds of dollars per month,and the price is the unit retail price for the particular month.Using MINITAB the following computer output is obtained. The regression equation is Sales = 31.0 + 0.820 Advertising - 0.325 Price + 1.84 Stores S = 5.465v R - Sq = 96.7% R - Sq(adj)= 95.0% Analysis of Variance Based on the multiple regression model given above,the point estimate of the monthly light fixture sales corresponding to second sample data is 49.82 or 49,820 units.This point estimate is calculated based on the assumption that the company spends $4000 on advertising,the price of the fixture is $60 and the fixture is being sold at 3 retail stores.Additional information related to this point estimate is given below. The 95% prediction interval for the point estimate given above is from 33.9 to 65.74.Interpret the meaning of this interval.

If it is desired to include marital status in a multiple regression model by using the categories: single,married,separated,divorced,widowed,what will be the effect on the model?

A member of the state legislature has expressed concern about the differences in the mathematics test scores of high school freshmen across the state.She asks her research assistant to conduct a study to investigate what factors could account for the differences.The research assistant looked at a random sample of school districts across the state and used the factors of percentage of mathematics teachers in each district with a degree in mathematics,the average age of mathematics teachers and the average salary of mathematics teachers s = 7.62090 Analysis of Variance Calculate the adjusted R².

A particular multiple regression model has 3 independent variables,the sum of the squared error is 7680,and the total number of observations is 34.What is the value of the standard error of estimate?

Consider the following partial computer output for a multiple regression model. Analysis of Variance What is the mean square error?

The difference between the observed values of y and the predicted value of y is referred to as a/an _____.

A member of the state legislature has expressed concern about the differences in the mathematics test scores of high school freshmen across the state.She asks her research assistant to conduct a study to investigate what factors could account for the differences.The research assistant looked at a random sample of school districts across the state and used the factors of percentage of mathematics teachers in each district with a degree in mathematics,the average age of mathematics teachers and the average salary of mathematics teachers s = 7.62090 Analysis of Variance Additional information related to this point estimate of 65.12 is given below. Predicted Values for New Observations 50% with math degree,average age of 43 and average salary is 48.3 New Calculate the 95% prediction interval for this point estimate.