Exam 12: Linear Regression and Correlation

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Given the following five points: (-2,0), (-1,0), (0,1), (1,1), and (2,3). What is the Y intercept?

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A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. To verify this believe, the following data was collected: A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. To verify this believe, the following data was collected:     The 95% prediction interval for a particular person making 30 calls is: A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. To verify this believe, the following data was collected:     The 95% prediction interval for a particular person making 30 calls is: The 95% prediction interval for a particular person making 30 calls is:

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   What is the independent variable? What is the independent variable?

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  -What is the standard error of estimate?____________ -What is the standard error of estimate?____________

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When comparing the 95% confidence and prediction intervals for a given regression analysis,

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We have collected price per share and dividend information from a sample of 30 companies. We have collected price per share and dividend information from a sample of 30 companies.    The slope in this instance indicates: The slope in this instance indicates:

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i. Perfect correlation means that the scatter diagram will appear as a straight line ii. If the coefficient of correlation is 0.80, the coefficient of determination is 0.64. iii. The coefficient of determination can assume values between 0% and 100%

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The partial megastat output below is regression analysis of the relationship between annual payroll and number of wins in a season for 28 teams in professional sports. The purpose of the analysis Is to predict the number of wins when given an annual payroll in $millions. Although technically not a sample, the baseball data below will be treated as a convenience sample of all major league professional sports. The partial megastat output below is regression analysis of the relationship between annual payroll and number of wins in a season for 28 teams in professional sports. The purpose of the analysis Is to predict the number of wins when given an annual payroll in $millions. Although technically not a sample, the baseball data below will be treated as a convenience sample of all major league professional sports.   Refer to the printout above. How many independent variables? Refer to the printout above. How many independent variables?

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i. Trying to predict weekly sales with a standard error of estimate of $1,955, we would conclude that 68 percent of the predictions would not be off more than $1,955, 95 percent would not be off by more $3,910, and 99.7 percent would not be off by more than $5,865. T6 Ii) The smaller the sample, the smaller the possible error as measured by the standard error of estimate. F6 Iii) Approximately 95% of the values lie within two standard errors of the regression line.

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A regression analysis yields the following information: Y' = 2.24 + 1.49 X S y x = 1.66; ∑x = 32; ∑x2 = 134; n = 10 Compute the 95% confidence interval when X = 4.

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i. If there is absolutely no relationship between two variables, what will Pearson's r equal? ii. If the value of r is -0.96, what does this indicate about the dependent variable as the independent variable increases? Iii) What is the value of the correlation coefficient if there is perfect correlation?

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  -What is the Y intercept of the linear equation?____________ -What is the Y intercept of the linear equation?____________

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Information was collected from employee records to determine whether there is an association between an employee's age and the number or workdays they miss. Excel results are summarized below: Information was collected from employee records to determine whether there is an association between an employee's age and the number or workdays they miss. Excel results are summarized below:    From this printout you determine: From this printout you determine:

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What is the coefficient of determination? What is the coefficient of determination?

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i. A coefficient of correlation r close to 0 (say, 0.08) shows that the relationship between two variables is quite weak. Ii) A coefficient of correlation of -0.96 indicates a very weak negative correlation. iii. The coefficient of determination can only be positive.

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Given the scatter diagram below, that shows the number of workdays absent per year based on the age of the employees, which of the following statements are true? Given the scatter diagram below, that shows the number of workdays absent per year based on the age of the employees, which of the following statements are true?

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Using a 95% significance level, what is the critical value for the F-statistic? Using a 95% significance level, what is the critical value for the F-statistic?

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i. The strength of the correlation between two variables depends on the sign of the coefficient of correlation. Ii) A coefficient of correlation r close to 0 (say, 0.08) shows that the relationship between two variables is quite weak. Iii) The coefficient of determination is found by taking the square root of the coefficient of correlation.

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  -What is the dependent variable (Y)? -What is the dependent variable (Y)?

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In correlation analysis, the independent variable is

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