Exam 10: Multiple Regression

Use the following to answer the questions below: 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 -Use the provided output to determine how many cars were in the sample.

Use the following to answer the questions below: 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 -One of the cars in the sample was a 5-year-old Hyundai Elantra with 87,100 miles being sold for $6,000. What is the predicted price of this car using the single predictor model? Round to three decimal places.

Use the following to answer the questions below: 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 -Is mileage a significant predictor of the price of used Hyundai Elantras, even after accounting for age?

Use the following to answer the questions below: 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 -Some of the information in the ANOVA table is missing. How many degrees of freedom should be listed in the "Residual Error" row?

Use the following to answer the questions below: Fast food restaurants are 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) -Interpret the coefficient of Sodium in context.

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 to answer the questions below: 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 ‪ -Interpret the coefficient of Town in context.

Use the following to answer the questions below: 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 ‪ -Predict the amount of electricity used on a Monday with a high temperature of 62°F. Use one decimal place in your answer.

Use the following to answer the questions below: 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 ‪ -Interpret the coefficient of Age in context.

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 the questions below: 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 ‪ -Which predictors are significant at the 5% level?

Use the following to answer the questions below: Fast food restaurants are 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) -Interpret for this model.

Use the following to answer the questions below: 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 ‪ -Interpret for this model.

Use the following to answer the questions below: Fast food restaurants are 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) -One of the menu items in the sample is the "McDouble," which has 390 calories, 12 grams of fat, 65 mg of cholesterol, and 850 mg of sodium. What is the predicted response for the McDouble? Round your answer to two decimal places.

Use the following to answer the questions below: 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 ‪ -Predict the amount of electricity used on a Saturday with a high temperature of 68°F. Use one decimal place in your answer.

Use the following to answer the questions below: 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. The regression equation is Calories = 6.7 + 9.61 Fat (g) + 3.43 Carbs (g) + 4.42 Protein (g) -How many drinks were used in this sample?

A histogram 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.

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.

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 to answer the questions below: 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 ‪ -Using α = 0.05, is the model effective according to the ANOVA test? Include all details of the test.