An administrator wants to investigate the relationship between the numbers of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was chosen, and the following data were collected. Distance to Work (miles) 2 4 6 6 9 8 10 12 12 15 Number of Days Absent 8 5 8 6 6 4 6 3 5 3 Develop the least square regression line to predict the number of days absent based on the distance to work. Enter the regression coefficients in xx.xxx format. Round the value to three decimals and use leading and trailing zero to exactly match the format. Include the negative sign (minus sign) if the coefficient is negative. Do not include plus sign in your response. For example, if the coefficient is +6.1563 then enter 06.156 as your answer, if the coefficient is -0.54765 then enter -00.548 and if the answer is -1.6435 then enter -01.644 Ŷ=b0+b1X Constant/intercept (b0) = Coefficient of X/slope (b1) = What would be the estimated number of days absent for the employees living 5 miles from the company? Enter your answer in xx.xx format. Round the value to two decimals and use leading and trailing zero to exactly match the format. Include the negative sign (minus sign) if the answer is negative. Do not include plus sign in your response. For example, if the answer is +6.1563 then enter 06.16, if the answer is -0.54765 then enter -00.55 and if the answer is 6.1 then enter 06.10 Your answer is = What is the 95% confidence interval for average number of days absent for employees living 5 miles from the company? Enter your answer in xx.xx format. Round the value to two decimals and use leading and trailing zero to exactly match the format. Include the negative sign (minus sign) if the answer is negative. Do not include plus sign in your response. For example, if the answer is +6.1563 then enter 06.16, if the answer is -0.54765 then enter -00.55 and if the answer is 6.1 then enter 06.10 The upper limit of the confidence interval is: The lower limit of the confidence interval is: What is the estimated increase in number of days absent for each additional mile of distance between home and work? Enter your answer in xx.xx format. Round the value to two decimals and use leading and trailing zero to exactly match the format. Include the negative sign (minus sign) if the answer is negative. Do not include plus sign in your response. For example, if the answer is +6.1563 then enter 06.16, if the answer is -0.54765 then enter -00.55 and if the answer is 6.1 then enter 06.10 Your answer is: What is the standard error of estimate? Enter your answer in xx.xx format. Round the value to two decimals and use leading and trailing zero to exactly match the format. Include the negative sign (minus sign) if the answer is negative. Do not include plus sign in your response. For example, if the answer is +6.1563 then enter 06.16, if the answer is -0.54765 then enter -00.55 as your answer, if the answer is 6.1 then enter 06.10 Your answer is: What is the estimated coefficient of correlation between number of days absent and distance to work? Enter your answer in 0.xx format. Round the value to two decimals and use leading and trailing zero to exactly match the format. Include the negative sign (minus sign) if the answer is negative. Do not include plus sign in your response. For example, if the answer is +0.9753 then enter 0.98, if the coefficient is -0.54765 then enter -0.55 and if the answer is 0.3 then enter 0.30 Your answer is: Does the estimated coefficient of correlation suggest a direct or indirect relationship between the number of days absent and distance to work? Enter “D” for direct and “I” for indirect relationship Your answer (D/I) is: What percentage of variation in number of days absent at work can be explained by the distance that the employee travels to work? Enter your answer in percentage and round it to the nearest integer. Do not include % sign in your answer Your answer is:
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
An administrator wants to investigate the relationship between the numbers of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was chosen, and the following data were collected.
|
Distance to Work (miles) |
2 |
4 |
6 |
6 |
9 |
8 |
10 |
12 |
12 |
15 |
|
Number of Days Absent |
8 |
5 |
8 |
6 |
6 |
4 |
6 |
3 |
5 |
3 |
- Develop the least square regression line to predict the number of days absent based on the distance to work.
Enter the regression coefficients in xx.xxx format. Round the value to three decimals and use leading and trailing zero to exactly match the format. Include the negative sign (minus sign) if the coefficient is negative. Do not include plus sign in your response. For example, if the coefficient is +6.1563 then enter 06.156 as your answer, if the coefficient is -0.54765 then enter -00.548 and if the answer is -1.6435 then enter -01.644
Ŷ=b0+b1X
Constant/intercept (b0) =
Coefficient of X/slope (b1) =
- What would be the estimated number of days absent for the employees living 5 miles from the company?
Enter your answer in xx.xx format. Round the value to two decimals and use leading and trailing zero to exactly match the format. Include the negative sign (minus sign) if the answer is negative. Do not include plus sign in your response. For example, if the answer is +6.1563 then enter 06.16, if the answer is -0.54765 then enter -00.55 and if the answer is 6.1 then enter 06.10
Your answer is =
- What is the 95% confidence interval for average number of days absent for employees living 5 miles from the company?
Enter your answer in xx.xx format. Round the value to two decimals and use leading and trailing zero to exactly match the format. Include the negative sign (minus sign) if the answer is negative. Do not include plus sign in your response. For example, if the answer is +6.1563 then enter 06.16, if the answer is -0.54765 then enter -00.55 and if the answer is 6.1 then enter 06.10
The upper limit of the confidence interval is:
The lower limit of the confidence interval is:
- What is the estimated increase in number of days absent for each additional mile of distance between home and work?
Enter your answer in xx.xx format. Round the value to two decimals and use leading and trailing zero to exactly match the format. Include the negative sign (minus sign) if the answer is negative. Do not include plus sign in your response. For example, if the answer is +6.1563 then enter 06.16, if the answer is -0.54765 then enter -00.55 and if the answer is 6.1 then enter 06.10
Your answer is:
- What is the standard error of estimate?
Enter your answer in xx.xx format. Round the value to two decimals and use leading and trailing zero to exactly match the format. Include the negative sign (minus sign) if the answer is negative. Do not include plus sign in your response. For example, if the answer is +6.1563 then enter 06.16, if the answer is -0.54765 then enter -00.55 as your answer, if the answer is 6.1 then enter 06.10
Your answer is:
- What is the estimated coefficient of
correlation between number of days absent and distance to work?
Enter your answer in 0.xx format. Round the value to two decimals and use leading and trailing zero to exactly match the format. Include the negative sign (minus sign) if the answer is negative. Do not include plus sign in your response. For example, if the answer is +0.9753 then enter 0.98, if the coefficient is -0.54765 then enter -0.55 and if the answer is 0.3 then enter 0.30
Your answer is:
- Does the estimated coefficient of correlation suggest a direct or indirect relationship between the number of days absent and distance to work?
Enter “D” for direct and “I” for indirect relationship
Your answer (D/I) is:
- What percentage of variation in number of days absent at work can be explained by the distance that the employee travels to work?
Enter your answer in percentage and round it to the nearest integer. Do not include % sign in your answer
Your answer is:
Step by step
Solved in 2 steps with 1 images
