A study was done to look at the relationship between number of vacation days employees take each year and the number of sick days they take each year. The results of the survey are shown below. Vacation Days 5 15 13 3 9 0 3 7 7 14 4 Sick Days 5 5 1 5 4 9 9 6 5 3 9 Interpret r2r2 : There is a 58% chance that the regression line will be a good predictor for the number of sick days taken based on the number of vacation days taken. Given any group with a fixed number of vacation d
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A study was done to look at the relationship between number of vacation days employees take each year and the number of sick days they take each year. The results of the survey are shown below.
Vacation Days | 5 | 15 | 13 | 3 | 9 | 0 | 3 | 7 | 7 | 14 | 4 |
---|---|---|---|---|---|---|---|---|---|---|---|
Sick Days | 5 | 5 | 1 | 5 | 4 | 9 | 9 | 6 | 5 | 3 | 9 |
Interpret r2r2 :
- There is a 58% chance that the regression line will be a good predictor for the number of sick days taken based on the number of vacation days taken.
- Given any group with a fixed number of vacation days taken, 58% of all of those employees will take the predicted number of sick days.
- 58% of all employees will take the average number of sick days.
- There is a large variation in the number of sick days employees take, but if you only look at employees who take a fixed number of vacation days, this variation on average is reduced by 58%.
please choose 1 correct answer
The equation of the linear regression line is:
ˆy^ = ? + ?x (Please show your answers to 3 decimal places)
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- A study was done to look at the relationship between number of movies people watch at the theater each year and the number of books that they read each year. The results of the survey are shown below. Movies 8 2 7 9 9 2 0 7 4 4 9 Books 0 8 0 0 0 4 9 0 1 0 0 Interpret r2r2 : 70% of all people watch about the same number of movies as they read books each year. There is a 70% chance that the regression line will be a good predictor for the number of books people read based on the number of movies they watch each year. Given any fixed number of movies watched per year, 70% of the population reads the predicted number of books per year. There is a large variation in the number books people read each year, but if you only look at people who watch a fixed number of movies each year, this variation on average is reduced by 70%. The equation of the linear regression line is: ˆyy^ = + xx (Please show your answers to two decimal places) Use the model to predict the…For a sample of 8 employees, a personnel director has collected the following data on ownership of company stock, y, versus years with the firm, x. X 6 12 14 6 9 13 15 9 Y 300 408 560 252 288 650 630 522 (a) Determine the least-squares regression line and interpret its slope(b) For an employee who has been with the firm 10 years, what is the predicted number of shares owned? (c) Is there a statistical significance between years of service and ownership of company stocks? (use α=0.05α=0.05)A sample multiple linear regression equation predicts the response variable y to be 87.62 at values of the predictor variables x1 = 5, x2 = 12, and x3 = 27. What is the estimated value of the conditional mean of y at x1 = 5, x2 = 12, and x3 = 27?
- A manufacturing company that produces laminate for countertops is interested in studying the relationship between the number of hours of training that an employee receives and the number of defects per countertop produced. Ten employees are randomly selected. The number of hours of training each employee has received is recorded and the number of defects on the most recent countertop produced is determined. The results are as follows. Hours of Training Defects per Countertop1 54 17 03 32 52 45 15 21 86 2 The estimated regression equation and the standard error are given. Defects per Countertop=6.717822−1.004950(Hours of Training)Se=1.229787 Suppose a new employee has had 1 hour of training. What would be the 90% prediction interval for the number of defects per countertop? Round your answer to two decimal places.A study was done to look at the relationship between number of movies people watch at the theater each year and the number of books that they read each year. The results of the survey are shown below. Movies 10 7 6 10 0 9 1 6 Books 0 0 -0 0 9 0 9 -0 r2r2 = (Round to two decimal places) Interpret r2r2 : There is a 82% chance that the regression line will be a good predictor for the number of books people read based on the number of movies they watch each year. 82% of all people watch about the same number of movies as they read books each year. There is a large variation in the number books people read each year, but if you only look at people who watch a fixed number of movies each year, this variation on average is reduced by 82%. Given any fixed number of movies watched per year, 82% of the population reads the predicted number of books per year. The equation of the linear regression line is: ˆyy^ = + xx (Please show your answers to two decimal places)A sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of 10 salespersons. Salesperson Years of Experience Annual Sales ($1000s) 1 1 80 2 3 97 3 4 92 4 4 102 5 6 103 6 8 111 7 10 119 8 10 123 9 11 117 10 13 136 Develop a scatter diagram for these data with years of experience as the independent variable. Develop an estimated regression equation that can be used to predict annual sales given the years of experience. Use the estimated regression equation to predict annual sales for a salesperson with 9 years of experience.
- A company trains its employees with instructional videos and claims that the amount of time, in hours, spent training is linearly related to an increase in productivity. The company selected a random sample of five employees to test its claim. The data were used to create the computer output for a least-squares linear regression, shown in the table. Variable DF Estimate SE Intercept 1 3.6 1.1489 Hours 1 0.8 0.3464 Which of the following is the correct test statistic and number of degrees of freedom? t=2.31 with 4 degrees of freedom A t=2.31 with 3 degrees of freedom B t=2.31 with 5 degrees of freedom C t=3.13 with 1 degree of freedom D t=3.13 with 3 degrees of freedom EA manufacturer of car batteries claims that the mean lifetime of their battery is 67 months. Thinking that this claim is inflated, graduate students buy a random sample of 72 car batteries from this manufacturer. How should they proceed? a) Perform a hypothesis test of H0:μ=67 versus Ha:μ>67 b) Perform a hypothesis test of H0:μ=67 versus Ha:μ<67 c) Use Simple linear regressionThe following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars. Predictor Coefficient SE Coefficient t p-value Constant 7.096 3.245 2.187 0.010 x1 0.222 0.117 1.897 0.000 x2 − 1.024 0.562 − 1.822 0.028 x3 − 0.337 0.192 − 1.755 0.114 x4 0.623 0.263 2.369 0.001 x5 − 0.058 0.029 − 2.000 0.112 Analysis of Variance Source DF SS MS F p-value Regression 5 2,009.28 401.9 7.33 0.000 Residual Error 50 2,741.54 54.83 Total 55 4,750.81 x1 is the number of architects employed by the company. x2 is the number of engineers employed by the company. x3 is the number of years involved with health care projects. x4 is the number of states in which the firm operates. x5 is the percent of the firm’s work that is health care−related. Write out…
- The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars. Predictor Coefficient SE Coefficient t p-value Constant 7.096 3.245 2.187 0.010 x1 0.222 0.117 1.897 0.000 x2 − 1.024 0.562 − 1.822 0.028 x3 − 0.337 0.192 − 1.755 0.114 x4 0.623 0.263 2.369 0.001 x5 − 0.058 0.029 − 2.000 0.112 Analysis of Variance Source DF SS MS F p-value Regression 5 2,009.28 401.9 7.33 0.000 Residual Error 50 2,741.54 54.83 Total 55 4,750.81 x1 is the number of architects employed by the company. x2 is the number of engineers employed by the company. x3 is the number of years involved with health care projects. x4 is the number of states in which the firm operates. x5 is the percent of the firm’s work that is health care−related. Write out…The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars. Predictor Coefficient SE Coefficient t p-value Constant 7.096 3.245 2.187 0.010 x1 0.222 0.117 1.897 0.000 x2 − 1.024 0.562 − 1.822 0.028 x3 − 0.337 0.192 − 1.755 0.114 x4 0.623 0.263 2.369 0.001 x5 − 0.058 0.029 − 2.000 0.112 Analysis of Variance Source DF SS MS F p-value Regression 5 2,009.28 401.9 7.33 0.000 Residual Error 50 2,741.54 54.83 Total 55 4,750.81 x1 is the number of architects employed by the company. x2 is the number of engineers employed by the company. x3 is the number of years involved with health care projects. x4 is the number of states in which the firm operates. x5 is the percent of the firm’s work that is health care−related. c-1. At the…The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars. Predictor Coefficient SE Coefficient t p-value Constant 7.987 2.967 2.690 0.010 x1 0.122 0.031 3.920 0.000 x2 − 1.120 0.053 − 2.270 0.028 x3 − 0.063 0.039 − 1.610 0.114 x4 0.523 0.142 3.690 0.001 x5 − 0.065 0.040 − 1.620 0.112 Analysis of Variance Source DF SS MS F p-value Regression 5 371000 742 12.89 0.000 Residual Error 46 2647.38 57.55 Total 51 6357.38 x1 is the number of architects employed by the company. x2 is the number of engineers employed by the company. x3 is the number of years involved with health care projects. x4 is the number of states in which the firm operates. x5 is the percent of the firm’s work that is health care–related. Write out the…