A sales manager collected the following data on x = years of experience and y = annual sales ($1,000s). The estimated regression equation for these data is ŷ = 80 + 4x. Salesperson Years ofExperience Annual Sales($1,000s) 1 1 80 2 3 97 3 4 97 4 4 102 5 6 103 6 8 101 7 10 119 8 10 118 9 11 127 10 13 136 (a) Compute SST, SSR, and SSE. SST = SSR = SSE = (b) Compute the coefficient of determination r2. (Round your answer to three decimal places.) r2 = Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line. The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line. The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line. The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line. (c) What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)
A sales manager collected the following data on x = years of experience and y = annual sales ($1,000s). The estimated regression equation for these data is ŷ = 80 + 4x. Salesperson Years ofExperience Annual Sales($1,000s) 1 1 80 2 3 97 3 4 97 4 4 102 5 6 103 6 8 101 7 10 119 8 10 118 9 11 127 10 13 136 (a) Compute SST, SSR, and SSE. SST = SSR = SSE = (b) Compute the coefficient of determination r2. (Round your answer to three decimal places.) r2 = Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line. The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line. The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line. The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line. (c) What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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.
Question
A sales manager collected the following data on x = years of experience and y = annual sales ($1,000s). The estimated regression equation for these data is
ŷ = 80 + 4x.
| Salesperson | Years of Experience |
Annual Sales ($1,000s) |
|---|---|---|
| 1 | 1 | 80 |
| 2 | 3 | 97 |
| 3 | 4 | 97 |
| 4 | 4 | 102 |
| 5 | 6 | 103 |
| 6 | 8 | 101 |
| 7 | 10 | 119 |
| 8 | 10 | 118 |
| 9 | 11 | 127 |
| 10 | 13 | 136 |
(a)
Compute SST, SSR, and SSE.
SST = SSR = SSE =
(b)
Compute the coefficient of determination
r2.
(Round your answer to three decimal places.)r2
=Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.)
The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line. The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line. The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line. The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line.
(c)
What is the value of the sample correlation coefficient ? (Round your answer to three decimal places.)
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