Exam 10: Multiple Regression

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 -Is the model effective according to the ANOVA test? Use = 0.05. Include all details of the test.

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 -How many points are the Timberwolves predicted to score in a home game? Round to one decimal place.

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. ‪ -Is the model effective according to the ANOVA test? Use a 5% significance level. 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 -Interpret R² for this model.

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. ‪ -How many drinks were used in this sample?

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 predictor appears to be the most important in this model? Explain briefly.

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 -Interpret the coefficient of Weekend in context.

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 be listed in the "Residual Error" row?

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 single predictor of the price of used Hyundai Elantras? Use = 0.05. Include all details of your test.

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 -Which predictors are significant at the 5% level? What are their p-values?

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 -Interpret the coefficient of Model in context.

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 -What is the predicted price of a 6-year-old Toyota Camry? Round to three decimal places.

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 -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.

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 -How many days are included in the sample?

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 -Interpret R² for this model.

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 -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 residual for the McDouble? Round your answer to two decimal places.

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 -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 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 the coefficient of Age in context.

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 -Is the model effective according to the ANOVA test? Use = 0.05. Include all details of the test.

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 -Using = 0.05, is there a difference in the number of points scored for home and away games? Include all details of the test.