Exam 23: Inferences for Regression

A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn.Eight similar Plots of land are selected and each is planted with a particular density of seed.One month Later the quality of each lawn is rated on a scale of 0 to 100.The regression analysis and Summary statistics are given below.Find a 99% confidence interval for the mean lawn Quality of all lawns sown with a seed density of 2.5. Variable Count Mean StdDev Seed Density 8 2.75 0.49099 Lawn Quality 8 45.625 3.712611 Dependent variable is: Lawn Quality $R$ squared $= 36.0\%$ $s = 9.073602$ with $8 - 2 = 6$ degrees of freedom Variable Coefficient s.e. of Coeff t-ratio prob Constant 31.14815 7.510757 4.413423 0.004503 Seed Density 4.537037 2.469522 1.837213 0.115825

A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn.Eight similar Plots of land are selected and each is planted with a particular density of seed.One month Later the quality of each lawn is rated on a scale of 0 to 100.The regression analysis is given Below.A 99% confidence interval for the mean lawn quality of all lawns sown with a seed Density of 3.5 was found to be (33.3, 60.8).Give an interpretation of this interval. Dependent variable is: Lawn quality $R$ squared $= 36.08$ $s = 9.073602$ with $8 - 2 = 6$ degrees of freedom Variable Coefficient s.e. of Coeff t-ratio prob Constant 31.14815 7.510757 4.413423 0.004503 Seed Density 4.537037 2.469522 1.837213 0.115825

Selling price and amount spent advertising were entered into a multiple regression to determine what affects flat panel LCD TV sales.Using the output below, calculated F Statistic to determine the overall significance of the estimated multiple regression model is

Applicants for a particular job, which involves extensive travel in Spanish-speaking countries, must take a proficiency test in Spanish.The sample data were obtained in a study Of the relationship between the numbers of years applicants have studied Spanish and their Score on the test.Use the regression analysis and summary statistics given below to find a 95% confidence interval for the mean score of all applicants who have studied Spanish for 3.1 years. Variable Count Mean StdDev Years 10 3.5 0.341565 Score 10 69.7 4.088058 Dependent variable is: Score $\mathrm { R }$ squared $= 83.0$ \% $s = 5.65138$ with $10 - 2 = 8$ degrees of freedom Variable Coefficient s.e. of Coeff t-ratio prob Constant 31.53333 6.360418 4.957745 0.00111 Number of years 10.90476 1.744054 6.252538 0.000245

Applicants for a particular job, which involves extensive travel in Spanish-speaking countries, must take a proficiency test in Spanish.The sample data were obtained in a study Of the relationship between the numbers of years applicants have studied Spanish and their Score on the test.Use the regression analysis given below to find a 99% confidence interval For the slope of the regression line. Dependent variable is: Score $\mathrm { R }$ squared $= 83.0$ 웅 $s = 5.65138$ with $10 - 2 = 8$ degrees of freedom Variable Coefficient s.e. of Coeff t-ratio prob Constant 31.53333 6.360418 4.957745 0.00111 Number of years 10.90476 1.744054 6.252538 0.000245

A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn.Eight similar Plots of land are selected and each is planted with a particular density of seed.One month Later the quality of each lawn is rated on a scale of 0 to 100.The regression analysis is given Below. Dependent variable is: Lawn Quality $R$ squared $= 36.0$ 웅 $s = 9.073602$ with $8 - 2 = 6$ degrees of freedom Variable Coefficient s.e. of Coeff t-ratio prob Constant 31.14815 7.510757 4.413423 0.004503 Seed Density 4.537037 2.469522 1.837213 0.115825

A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn.Eight similar Plots of land are selected and each is planted with a particular density of seed.One month Later the quality of each lawn is rated on a scale of 0 to 100.The regression analysis is given Below.A 99% prediction interval for the lawn quality of a lawn sown with a seed density of 1.9 was determined to be (5.3, 78.3).Give an interpretation of this interval. Dependent variable is: Lawn Quality $R$ squared $= 36.0$ 웅 $s = 9.073602$ with $8 - 2 = 6$ degrees of freedom Variable Coefficient s.e. of Coeff t-ratio prob Constant 31.14815 7.510757 4.413423 0.004503 Seed Density 4.537037 2.469522 1.837213 0.115825

A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn.Eight similar Plots of land are selected and each is planted with a particular density of seed.One month Later the quality of each lawn is rated on a scale of 0 to 100.The regression analysis is given Below.A 95% confidence interval for the slope of the regression line was determined to be (-1.51, 10.58).Give an interpretation of this interval. Dependent variable is: Lawn Quality $R$ squared $= 36.0$ 8 $s = 9.073602$ with $8 - 2 = 6$ degrees of freedom Variable Coefficient s.e. of Coeff t-ratio prob Constant 31.14815 7.510757 4.413423 0.004503 Seed Density 4.537037 2.469522 1.837213 0.115825

A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn.Eight similar Plots of land are selected and each is planted with a particular density of seed.One month Later the quality of each lawn is rated on a scale of 0 to 100.The regression analysis and Summary statistics are given below.Determine a 99% prediction interval for the lawn quality Of a lawn sown with a seed density of 2.9. Variable Count Mean StdDev Seed Density 8 2.75 0.49099 Lawn Quality 8 45.625 3.712611 Dependent variable is: Lawn Quality $R$ squared $= 36.0 \%$ $s = 9.073602$ with $8 - 2 = 6$ degrees of freedom Variable Coefficient s.e. of Coeff t-ratio prob Constant 31.14815 7.510757 4.413423 0.004503 Seed Density 4.537037 2.469522 1.837213 0.115825

A sample of 33 companies was randomly selected and data collected on the average annual bonus, turnover rate (%), and trust index (measured on a scale of 0 - 100).According to the Output is shown below, what is the estimated multiple regression model? Dependent Variable is Turnover Rate Predictor Coef SE Coef T P Constant 12.1005 0.7826 15.46 0.000 Trust Index -0.07149 0.01966 -3.64 0.001 Average Bonus -0.0007216 0.0001481 -4.87 0.000

Applicants for a particular job, which involves extensive travel in Spanish-speaking countries, must take a proficiency test in Spanish.The sample data were obtained in a study Of the relationship between the numbers of years applicants have studied Spanish and their Score on the test.A 95% confidence interval for the mean score of all applicants who have Studied Spanish for 4.6 years was determined to be (75.6, 87.7).Give an interpretation of this Interval. Dependent variable is: Score $R$ squared $= 83.09$ $s = 5.65138$ with $10 - 2 = 8$ degrees of freedom Variable Coefficient s.e. of Coeff t-ratio prob Constant 31.53333 6.360418 4.957745 0.00111 Number of years 10.90476 1.744054 6.252538 0.000245

Applicants for a particular job, which involves extensive travel in Spanish-speaking countries, must take a proficiency test in Spanish.The sample data were obtained in a study Of the relationship between the numbers of years applicants have studied Spanish and their Score on the test.Use the regression analysis and summary statistics given below to find a 95% prediction interval for the score of an applicant who has studied Spanish for 3.1 years. Variable Count Mean StdDev Years 10 3.5 0.341565 Score 10 69.7 4.088058 Dependent variable is: Score $R$ squared $= 83.0 \%$ $s = 5.65138$ with $10 - 2 = 8$ degrees of freedom Variable Coefficient s.e. of Coeff t-ratio prob Constant 31.53333 6.360418 4.957745 0.00111 Number of years 10.90476 1.744054 6.252538 0.000245

Applicants for a particular job, which involves extensive travel in Spanish-speaking countries, must take a proficiency test in Spanish.The sample data were obtained in a study Of the relationship between the numbers of years applicants have studied Spanish and their Score on the test.

Applicants for a particular job, which involves extensive travel in Spanish-speaking countries, must take a proficiency test in Spanish.The sample data were obtained in a study Of the relationship between the numbers of years applicants have studied Spanish and their Score on the test.A 99% confidence interval for the slope of the regression line was Determined to be (5.05, 16.76).Give an interpretation of this interval. Dependent variable is: Score $R$ squared $= 83.0 \%$ $s = 5.65138$ with $10 - 2 = 8$ degrees of freedom Variable Coefficient s.e. of Coeff t-ratio prob Constant 31.53333 6.360418 4.957745 0.00111 Number of years 10.90476 1.744054 6.252538 0.000245

Applicants for a particular job, which involves extensive travel in Spanish-speaking countries, must take a proficiency test in Spanish.The sample data were obtained in a study Of the relationship between the numbers of years applicants have studied Spanish and their Score on the test.A 95% prediction interval for the score of an applicant who has studied Spanish for 4.4 years was determined to be (65.4, 93.6).Give an interpretation of this Interval. Dependent variable is: Score $R$ squared $= 83.0$ 웋 $s = 5.65138$ with $10 - 2 = 8$ degrees of freedom Variable Coefficient s.e. of Coeff t-ratio prob Constant 31.53333 6.360418 4.957745 0.00111 Number of years 10.90476 1.744054 6.252538 0.000245

A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn.Eight similar Plots of land are selected and each is planted with a particular density of seed.One month Later the quality of each lawn is rated on a scale of 0 to 100.The regression analysis is given Below.Find a 95% confidence interval for the slope of the regression line. Dependent variable is: Lawn Quality $R$ squared $= 36.0$ 움 $s = 9.073602$ with $8 - 2 = 6$ degrees of freedom Variable Coefficient s.e. of Coeff t-ratio prob Constant 31.14815 7.510757 4.413423 0.004503 Seed Density 4.537037 2.469522 1.837213 0.115825