Exam 9: Inference for Regression

Use the following 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 area. They want to predict the selling price of homes (in thousands of dollars) based on the age of the home (in years). Some summary statistics, partial regression output, and a scatterplot of the relationship (with regression line) are provided. Use two decimal places when reporting the results from any calculations, unless otherwise specified. The regression equation is Price (in thousands) = 193 - 0.665 Age Analysis of Variance -Use the information in the computer output to compute the standard error of the slope, SE. Report your answer with four decimal places.

Use the following 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 area. They want to predict the selling price of homes (in thousands of dollars) based on the age of the home (in years). Some summary statistics, partial regression output, and a scatterplot of the relationship (with regression line) are provided. Use two decimal places when reporting the results from any calculations, unless otherwise specified. The regression equation is Price (in thousands) = 193 - 0.665 Age Analysis of Variance -Compute the t test statistic for the slope.

Use the following A quantitatively savvy, young couple is interested in purchasing a home in northern New York. They collected data on 48 houses that had recently sold in the area. They want to predict the selling price of homes (in thousands of dollars) based on the size of the home (in square feet). The regression equation is Price (in thousands) = 17.1 + 0.0643 Size (sq. ft.) S = 48.5733 R-Sq = 37.5% R-Sq(adj) = 36.1% Predicted Values for New Observations -Construct and interpret a 95% confidence interval for the population slope.

Use the following Students in a small statistics course wanted to investigate if forearm length (in cm) was useful for predicting foot length (in cm). The data they collected are displayed in the provided scatterplot (with regression), and the computer output from the analysis is provided. Use three decimal places when reporting the results from any calculations, unless otherwise specified. The regression equation is Foot (cm) = 9.22 + 0.574 Forearm (cm) Predicted Values for New Observations -When conducting inference for the population slope, it is most common to test if the population slope is different from zero. However, there are other situations where a different test might be more interesting. For instance, it is often said that the length of the forearm is roughly the same as the length of the foot (see, for example, the movie Pretty Woman). What population slope is implied by this statement, and what would the hypotheses for testing the accuracy of this claim look like?

Use the following A quantitatively savvy, young couple is interested in purchasing a home in northern New York. They collected data on 48 houses that had recently sold in the area. They want to predict the selling price of homes (in thousands of dollars) based on the size of the home (in square feet). The regression equation is Price (in thousands) = 17.1 + 0.0643 Size (sq. ft.) S = 48.5733 R-Sq = 37.5% R-Sq(adj) = 36.1% Predicted Values for New Observations -Use the computer output to provide and interpret a 95% interval for the selling price of a single 2,000 square foot house in this portion of northern New York.

Use the following In recent years, fast food restaurants have been required to publish nutrition information about the foods they serve. Nutrition information about a random sample of McDonald's lunch/dinner menu items (excluding sides and drinks) was obtained from their website. We wish to use the sodium content (in milligrams) to better understand the number of calories in the lunch/dinner menu items at McDonald's. Some summary statistics, partial computer output from a regression analysis, and a scatterplot (with regression line) of the data are provided. Use two decimal places when reporting the results from any calculations, unless otherwise specified. The regression equation is Calories = 99.69 + 0.3698 Sodium (mg) -Write down the equation of the least squares line and use it to predict the number of calories in a lunch/dinner menu item with 1,000 mg of sodium.

Use the following In recent years, fast food restaurants have been required to publish nutrition information about the foods they serve. Nutrition information about a random sample of 15 McDonald's lunch/dinner menu items (excluding sides and drinks) was obtained from their website. We wish to use the total fat content (in grams) to better understand the number of calories in the lunch/dinner menu items at McDonald's. Computer output from a regression analysis and a scatterplot (with regression line) of the data are provided. Use two decimal places when reporting the results from any calculations, unless otherwise specified. -The website also provides information about the sugar content in the menu items at McDonald's. For this sample of 15 lunch/dinner menu items, the correlation between number of calories and sugar content (in grams) is 0.35. Test, at the 5% significance level, if there is a significant linear association between number of calories and sugar content for McDonald's lunch/dinner menu items. Include all details of the test. Round the test statistic to three decimal places.

Use the following Students in a small statistics course wanted to investigate if forearm length (in cm) was useful for predicting foot length (in cm). The data they collected are displayed in the provided scatterplot (with regression), and the computer output from the analysis is provided. Use three decimal places when reporting the results from any calculations, unless otherwise specified. The regression equation is Foot (cm) = 9.22 + 0.574 Forearm (cm) Predicted Values for New Observations -Use the ANOVA table to determine the overall sample size.

Use the following In recent years, fast food restaurants have been required to publish nutrition information about the foods they serve. Nutrition information about a random sample of 15 McDonald's lunch/dinner menu items (excluding sides and drinks) was obtained from their website. We wish to use the total fat content (in grams) to better understand the number of calories in the lunch/dinner menu items at McDonald's. Computer output from a regression analysis and a scatterplot (with regression line) of the data are provided. Use two decimal places when reporting the results from any calculations, unless otherwise specified. -Write down the equation of the least squares line and use it to predict the number of calories in a menu item with 20 grams of fat.

Use the following Data were collected on the age (in years) and price (in thousands of dollars) of a random sample of 25 used Hyundai Elantras. A scatterplot of the data (with regression line) and computer output from a regression analysis are provided. Use three decimal places when reporting the results from any calculations, unless otherwise specified. The regression equation is Price = 15.3 - 1.71 Age S = 1.37179 R-Sq = 88.9% R-Sq(adj) = 88.4% Predicted Values for New Observations -Use the scatterplot to determine whether we should have any serious concerns about the conditions being met for using a linear model with these data. Explain briefly.

Use the following Computer output from a regression analysis is provided. ‪ -Use the p-value for testing if the slope in the population is different from zero (and a 5% significance level) to make a clear conclusion about the effectiveness of the model.

Use the following Data were collected on GPA and number of Facebook friends for students in a small statistics class. Some summary statistics, partial output from the regression analysis, and a scatterplot of the data (with regression line) are provided. Assume that students in this class are typical of all students at the university. Use three decimal places when reporting the results from any calculations, unless otherwise specified. The regression equation is GPA = 3.830 - 0.000919 FacebookFriends -Compute the t test statistic for the slope.

In a random sample of 41 students, the correlation between Math SAT score and college GPA is 0.289. Is there a significant linear association between Math SAT score and college GPA? Use = 0.05. Include all details of the test. Round the test statistic to two decimal places.

Use the following In recent years, fast food restaurants have been required to publish nutrition information about the foods they serve. Nutrition information about a random sample of 15 McDonald's lunch/dinner menu items (excluding sides and drinks) was obtained from their website. We wish to use the total fat content (in grams) to better understand the number of calories in the lunch/dinner menu items at McDonald's. Computer output from a regression analysis and a scatterplot (with regression line) of the data are provided. Use two decimal places when reporting the results from any calculations, unless otherwise specified. -Use the scatterplot to determine whether we should have any major concerns about the conditions being met for using a linear model with these data. Explain briefly.

Use the following Students in a small statistics course wanted to investigate if forearm length (in cm) was useful for predicting foot length (in cm). The data they collected are displayed in the provided scatterplot (with regression), and the computer output from the analysis is provided. Use three decimal places when reporting the results from any calculations, unless otherwise specified. The regression equation is Foot (cm) = 9.22 + 0.574 Forearm (cm) Predicted Values for New Observations -What is the test statistic for a test of the slope? What is the p-value? What is the conclusion of the test, in context?

Use the following Data were collected on the mileage (in thousands of miles) and price (in thousands of dollars) of a random sample of used Hyundai Elantras. A scatterplot of the data (with regression line), some summary statistics, and partial computer output from a regression analysis are provided. Use three decimal places when reporting the results from any calculations, unless otherwise specified. The regression equation is Price = 13.8 - 0.0912 Mileage -Use the provided output to construct and interpret a 95% interval for the price of a single used Hyundai Elantra with 50,000 miles.

Use the following In recent years, fast food restaurants have been required to publish nutrition information about the foods they serve. Nutrition information about a random sample of 15 McDonald's lunch/dinner menu items (excluding sides and drinks) was obtained from their website. We wish to use the total fat content (in grams) to better understand the number of calories in the lunch/dinner menu items at McDonald's. Computer output from a regression analysis and a scatterplot (with regression line) of the data are provided. Use two decimal places when reporting the results from any calculations, unless otherwise specified. -Use the computer output, and = 0.05, to test the slope to determine whether total fat content (g) is an effective predictor of the number of calories. Include all details of the test.

Use the following Data were collected on the age (in years) and price (in thousands of dollars) of a random sample of 25 used Hyundai Elantras. A scatterplot of the data (with regression line) and computer output from a regression analysis are provided. Use three decimal places when reporting the results from any calculations, unless otherwise specified. The regression equation is Price = 15.3 - 1.71 Age S = 1.37179 R-Sq = 88.9% R-Sq(adj) = 88.4% Predicted Values for New Observations -What is the estimated slope in this regression model? Interpret the slope in context.

Use the following In recent years, fast food restaurants have been required to publish nutrition information about the foods they serve. Nutrition information about a random sample of McDonald's lunch/dinner menu items (excluding sides and drinks) was obtained from their website. We wish to use the sodium content (in milligrams) to better understand the number of calories in the lunch/dinner menu items at McDonald's. Some summary statistics, partial computer output from a regression analysis, and a scatterplot (with regression line) of the data are provided. Use two decimal places when reporting the results from any calculations, unless otherwise specified. The regression equation is Calories = 99.69 + 0.3698 Sodium (mg) -Use the information in the computer output to compute the standard error of the slope, SE. Report your answer with four decimal places.

Use the following Data were collected on GPA and number of Facebook friends for students in a small statistics class. Some summary statistics, partial output from the regression analysis, and a scatterplot of the data (with regression line) are provided. Assume that students in this class are typical of all students at the university. Use three decimal places when reporting the results from any calculations, unless otherwise specified. The regression equation is GPA = 3.830 - 0.000919 FacebookFriends -Use the information in the ANOVA table to determine the number of students included in the dataset.