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Q11-15E

Expert-verifiedFound in: Page 653

Book edition
13th

Author(s)
James T. McClave, P. George Benson, Terry Sincich

Pages
888 pages

ISBN
9780134506593

**Refer to Exercise 11.14. After the least-squares line has been obtained, the table below (which is similar to Table 11.2) can be used for (1) comparing the observed and the predicted values of y and (2) computing SSE. **

**a. Complete the table. **

**b. Plot the least-squares line on a scatterplot of the data. Plot the following line on the same graph:**

** $\widehat{\mathbf{\text{y}}}\mathbf{\text{= 14 - 2.5x.}}$**

**c. Show that SSE is larger for the line in part b than for the least-squares line.**

**Answer **

- Fig. 1 Table.
- Fig. 2 Table, Fig. 3 Scatterplot diagram.
- SSE is smaller than the least square.

The line that minimizes the squared sum of residuals is known as the Least Squares Regression Line. By subtracting** $\widehat{\text{y}}$ **from y, the residual is the vertical distance between the observed and anticipated points.

From exercise 11.14, we have

$\widehat{\mathbf{\text{y}}}{\mathbf{\text{=1.78 +}}}\mathbf{(}\mathbf{-}\mathbf{\text{0.77}}\mathbf{)}{\mathbf{\text{x}}}$

$\widehat{\mathbf{\text{y}}}{\mathbf{\text{= 14}}}{\mathbf{-}}{\mathbf{\text{2.5x.}}}$

By putting the x value in the above equation, we get $\widehat{\text{y}}:$

SSE of $\widehat{\mathbf{\text{y}}}{\mathbf{\text{= 14}}}{\mathbf{-}}{\mathbf{\text{2.5x}}}$ is smaller than the least square, i.e.

108 < 153.6.39

**Therefore, SSE is smaller than the least square.**

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