Exam 10: Multiple Regression

Use the following Does the price of used cars depend upon the model? Data were collected on the selling price and age of used Hyundai Elantras (coded as Model = 1) and Toyota Camrys (coded as Model = 0). Output from the multiple regression analysis is provided. The regression equation is Price = 14.5 - 0.619 Age - 3.63 Model S = 2.63465 R-Sq = 69.3% R-Sq(adj) = 68.4% Analysis of Variance -Which of the following scatterplots of the residuals versus the predicted values does not indicate problems with either the linearity or the consistent variability conditions?

Use the following While many people count calories, some often don't think about calories in the beverages they consume. Starbucks, one of the leading coffeehouse chains, provides nutrition information about all of their beverages on their website. Nutrition information, including number of calories, fat (g), carbohydrates (g), and protein (g), was collected on a random sample of Starbucks' 16 ounce ("Grande") hot espresso drinks. Note that all of the drinks in the sample are made with 2% milk unless the name specifically included the term "Skinny," which is how Starbucks indicated a beverage made with nonfat milk. ‪ -Interpret the coefficient of Fat in context.

Use the following to answer questions : A quantitatively savvy, young couple is interested in purchasing a home in northern New York. They collected data on houses that had recently sold in the two towns they are considering. The variables they collected are the selling price of the home (in thousands of dollars), the size of the home (in square feet), the age of the home (in years), and the town in which the house is located (coded 1 = Canton and 0 = Potsdam). Output from their multiple regression analysis is provided. The regression equation is Price (in thousands) = 69.2 + 0.0627 Size (sq. ft.) - 0.632 Age + 1.6 Town S = 40.0763 R-Sq = 59.3% R-Sq(adj) = 56.5% Analysis of Variance -Interpret R² for this model.

Use the following The ANOVA table from a multiple regression analysis is provided. -Compute R² for this model. Round to three decimal places.

Use the following Output for a model to predict the GPAs of students at a small university based on their Math SAT scores, Verbal SAT scores, and the number of hours spent watching television in a typical week is provided. The regression equation is GPA = 1.80 + 0.00104 Math SAT + 0.00142 Verbal SAT - 0.0147 TV S = 0.366780 R-Sq = ?% R-Sq(adj) = 19.0% Analysis of Variance -Some of the information in the ANOVA table is missing. How many degrees of freedom should appear in the "Regression" row of the table?

Use the following to answer questions : A quantitatively savvy, young couple is interested in purchasing a home in northern New York. They collected data on houses that had recently sold in the two towns they are considering. The variables they collected are the selling price of the home (in thousands of dollars), the size of the home (in square feet), the age of the home (in years), and the town in which the house is located (coded 1 = Canton and 0 = Potsdam). Output from their multiple regression analysis is provided. The regression equation is Price (in thousands) = 69.2 + 0.0627 Size (sq. ft.) - 0.632 Age + 1.6 Town S = 40.0763 R-Sq = 59.3% R-Sq(adj) = 56.5% Analysis of Variance -Which predictors are significant at the 5% level? What are their p-values?

Use the following Is there such thing as a "home court/field advantage"? Especially at the professional level? The number of points scored and whether or not it was a home game are available for a sample of games played by the Minnesota Timberwolves during the 2011-2012 regular season. The Home variable is coded as 1 = home game and 0 = away game. The regression equation is Points Scored = 102 - 8.76 Home S = 12.7430 R-Sq = 11.5% R-Sq(adj) = 6.6% Analysis of Variance -Interpret the R² for this model.

Use the following to answer questions : A small university is concerned with monitoring the electricity usage in its Student Center, and its officials want to better understand what influences the amount of electricity used on a given day. They collected data on the amount of electricity used in the Student Center each day and the daily high temperature for nearly a year. They also made note of whether each day was a weekend or not (1 = Saturday/Sunday and 0 = Monday - Friday). Regression output is provided. Helpful notes: 1) electricity usage is measured in kilowatt hours, 2) during the cold months the Student Center is heated by gas, not electricity, and 3) air conditioning the building during the warm months does use electricity. The regression equation is Electricity = 83.6 + 0.529 High Temp - 25.2 Weekend S = 29.8162 R-Sq = 24.7% R-Sq(adj) = 24.2% Analysis of Variance -Predict the amount of electricity used on a Saturday with a high temperature of 68^o F. Use one decimal place in your answer.

Use the following to answer questions : Data were collected on the age (in years), mileage (in thousands of miles), and price (in thousands of dollars) of a random sample of used Hyundai Elantras. Output from two models are provided. Single Predictor Model: The regression equation is Price = 13.8 - 0.0912 Mileage Two Predictor Model: The regression equation is Price = 15.2 - 0.0101 Mileage - 1.55 Age S = 1.39445 R-Sq = 89.0% R-Sq(adj) = 88.0% Analysis of Variance -Regression output for the model that only uses Age as a predictor in the model is provided. Assuming that the residuals for this single predictor model do not indicate any problems, is this model an improvement over the model that uses both Age and Mileage as predictors? Statistically justify your answer by discussing at least two quantitative criteria. The regression equation is Price = 15.3 - 1.71 Age S = 1.37179 R-Sq = 88.9% R-Sq(adj) = 88.4% Analysis of Variance

Use the following In recent years, fast food restaurants have been required to publish nutrition information about the foods they serve. Nutrition information for a random sample of McDonald's lunch/dinner menu items (excluding sides and drinks) was obtained from their website. Output from a multiple regression analysis is provided. The regression equation is Calories = 65.2 + 9.46 Total Fat (g) + 0.876 Cholesterol (mg) + 0.131 Sodium (mg) S = 39.4529 R-Sq = 95.5% R-Sq(adj) = 94.3% Analysis of Variance -Interpret the coefficient of Sodium in context.

Use the following to answer questions : A quantitatively savvy, young couple is interested in purchasing a home in northern New York. They collected data on houses that had recently sold in the two towns they are considering. The variables they collected are the selling price of the home (in thousands of dollars), the size of the home (in square feet), the age of the home (in years), and the town in which the house is located (coded 1 = Canton and 0 = Potsdam). Output from their multiple regression analysis is provided. The regression equation is Price (in thousands) = 69.2 + 0.0627 Size (sq. ft.) - 0.632 Age + 1.6 Town S = 40.0763 R-Sq = 59.3% R-Sq(adj) = 56.5% Analysis of Variance -Regression output for a model that omits Town as a predictor is provided. Assuming that the residuals for this reduced model do not indicate any problems with using multiple regression, is this model an improvement over the model that uses Size, Age, and Town as predictors? Statistically justify your answer by discussing at least two quantitative criteria. The regression equation is Price (in thousands) = 70.6 + 0.0624 Size (sq. ft.) - 0.635 Age S = 39.6368 R-Sq = 59.3% R-Sq(adj) = 57.5% Analysis of Variance

Use the following Output for a model to predict the GPAs of students at a small university based on their Math SAT scores, Verbal SAT scores, and the number of hours spent watching television in a typical week is provided. The regression equation is GPA = 1.80 + 0.00104 Math SAT + 0.00142 Verbal SAT - 0.0147 TV S = 0.366780 R-Sq = ?% R-Sq(adj) = 19.0% Analysis of Variance -Use the output to determine how many students were included in the sample.

Use the following While many people count calories, some often don't think about calories in the beverages they consume. Starbucks, one of the leading coffeehouse chains, provides nutrition information about all of their beverages on their website. Nutrition information, including number of calories, fat (g), carbohydrates (g), and protein (g), was collected on a random sample of Starbucks' 16 ounce ("Grande") hot espresso drinks. Note that all of the drinks in the sample are made with 2% milk unless the name specifically included the term "Skinny," which is how Starbucks indicated a beverage made with nonfat milk. ‪ -A dotplot of the residuals and a scatterplot of the residuals versus the predicted values are provided. Discuss whether the conditions for a multiple linear regression are reasonable by referring to the appropriate plots.

Use the following Output for a model to predict the GPAs of students at a small university based on their Math SAT scores, Verbal SAT scores, and the number of hours spent watching television in a typical week is provided. The regression equation is GPA = 1.80 + 0.00104 Math SAT + 0.00142 Verbal SAT - 0.0147 TV S = 0.366780 R-Sq = ?% R-Sq(adj) = 19.0% Analysis of Variance -A dotplot of the residuals and a scatterplot of the residuals versus the predicted values are provided. Discuss whether the conditions for a multiple linear regression are reasonable by referring to the appropriate plots.

Use the following to answer questions : A quantitatively savvy, young couple is interested in purchasing a home in northern New York. They collected data on houses that had recently sold in the two towns they are considering. The variables they collected are the selling price of the home (in thousands of dollars), the size of the home (in square feet), the age of the home (in years), and the town in which the house is located (coded 1 = Canton and 0 = Potsdam). Output from their multiple regression analysis is provided. The regression equation is Price (in thousands) = 69.2 + 0.0627 Size (sq. ft.) - 0.632 Age + 1.6 Town S = 40.0763 R-Sq = 59.3% R-Sq(adj) = 56.5% Analysis of Variance -A dotplot of the residuals and a scatterplot of the residuals versus the predicted values are provided. Discuss whether the conditions for a multiple linear regression are reasonable by referring to the appropriate plots.

Use the following to answer questions : Data were collected on the age (in years), mileage (in thousands of miles), and price (in thousands of dollars) of a random sample of used Hyundai Elantras. Output from two models are provided. Single Predictor Model: The regression equation is Price = 13.8 - 0.0912 Mileage Two Predictor Model: The regression equation is Price = 15.2 - 0.0101 Mileage - 1.55 Age S = 1.39445 R-Sq = 89.0% R-Sq(adj) = 88.0% Analysis of Variance -Is the two predictor model effective according to the ANOVA test? Use = 0.05. Include all details of the test.

Use the following In recent years, fast food restaurants have been required to publish nutrition information about the foods they serve. Nutrition information for a random sample of McDonald's lunch/dinner menu items (excluding sides and drinks) was obtained from their website. Output from a multiple regression analysis is provided. The regression equation is Calories = 65.2 + 9.46 Total Fat (g) + 0.876 Cholesterol (mg) + 0.131 Sodium (mg) S = 39.4529 R-Sq = 95.5% R-Sq(adj) = 94.3% Analysis of Variance -A boxplot of the residuals and a scatterplot of the residuals versus the predicted values are provided. Discuss whether the conditions for a multiple linear regression are reasonable by referring to the appropriate plots.

Use the following Output for a model to predict the GPAs of students at a small university based on their Math SAT scores, Verbal SAT scores, and the number of hours spent watching television in a typical week is provided. The regression equation is GPA = 1.80 + 0.00104 Math SAT + 0.00142 Verbal SAT - 0.0147 TV S = 0.366780 R-Sq = ?% R-Sq(adj) = 19.0% Analysis of Variance -The R² for this model is missing in the provided output. Use the available information to compute (round to three decimal places) and interpret R² for this model.

Use the following to answer questions : Data were collected on the age (in years), mileage (in thousands of miles), and price (in thousands of dollars) of a random sample of used Hyundai Elantras. Output from two models are provided. Single Predictor Model: The regression equation is Price = 13.8 - 0.0912 Mileage Two Predictor Model: The regression equation is Price = 15.2 - 0.0101 Mileage - 1.55 Age S = 1.39445 R-Sq = 89.0% R-Sq(adj) = 88.0% Analysis of Variance -Is mileage a significant predictor of the price of used Hyundai Elantras, even after accounting for age? Explain briefly.

Use the following In recent years, fast food restaurants have been required to publish nutrition information about the foods they serve. Nutrition information for a random sample of McDonald's lunch/dinner menu items (excluding sides and drinks) was obtained from their website. Output from a multiple regression analysis is provided. The regression equation is Calories = 65.2 + 9.46 Total Fat (g) + 0.876 Cholesterol (mg) + 0.131 Sodium (mg) S = 39.4529 R-Sq = 95.5% R-Sq(adj) = 94.3% Analysis of Variance -Which predictors are significant at the 5% level? What are their p-values?