
a:
Regression equation.
a:

Explanation of Solution
The general regression equation can be written as follows:
The term
Table 1 shows the processing of data as follows:
Table 1
Sl | |||||
1 | -5 | 15 | 25 | 225 | -75 |
2 | -2 | 9 | 4 | 81 | -18 |
3 | 0 | 7 | 0 | 49 | 0 |
4 | 3 | 6 | 9 | 36 | 18 |
5 | 4 | 4 | 16 | 16 | 16 |
6 | 7 | 1 | 49 | 1 | 7 |
Total | 7 | 42 | 103 | 408 | -52 |
Standard deviation
Standard deviation is -202.2.
The variance of x
The variance of x is 18.97.
The value of coefficient ( b1) can be calculated as follows:
The value of b1 is -1.065.
The average value
The average value of x is 1.167.
The average value
The average value of x is 7.
Intercept b0 can be calculated as follows:
The intercept value is 8.253.
Thus, the regression equation is given below:
b:
The predicted value of y.
b:

Explanation of Solution
The estimated value of y
Table 2 shows the predicted value of x that is obtained using the regression equation with different levels of x values as follows:
Table 2
Sl | ||
1 | -5 | 13.58 |
2 | -2 | 10.38 |
3 | 0 | 8.253 |
4 | 3 | 5.058 |
5 | 4 | 3.993 |
6 | 7 | 0.758 |
c:
Calculate the residual.
c:

Explanation of Solution
The value of residual
Table 3 shows the residual value that is obtained using Equation (1) as follows:
Table 3
Sl | |||
1 | -5 | 13.58 | 1.42 |
2 | -2 | 10.38 | -1.38 |
3 | 0 | 8.253 | -1.253 |
4 | 3 | 5.058 | 0.942 |
5 | 4 | 3.993 | 0.007 |
6 | 7 | 0.758 | 0.202 |
d:
Calculate the standardized residual.
d:

Explanation of Solution
The variance of y
The variance of y is 22.8.
Error sum of square (SSE) can be calculated as follows:
Error sum of square is 6.451.
The value of
The value of
The value of standardized residual (se) can be calculated using the below equation:
Table 5 shows the standardized residual value that is obtained using Equation (2) as follows:
Table 5
Sl | se | |||
1 | -5 | 13.58 | 1.42 | 1.18 |
2 | -2 | 10.38 | -1.38 | -1.087 |
3 | 0 | 8.253 | -1.253 | -0.987 |
4 | 3 | 5.058 | 0.942 | 0.742 |
5 | 4 | 3.993 | 0.007 | 0.0055 |
6 | 7 | 0.758 | 0.202 | 0.159 |
e:
Identification of outliers.
e:

Explanation of Solution
From the above calculations, it is known that there are no outliers.
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Chapter 16 Solutions
Statistics for Management and Economics
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