Question

For the data set below,

(a) Determine the least-squares regression line.

(b) Compute the sum of the squared residuals for the least-squares
regression line.

x 20 30 40 50 60

___________________

y 106 95 82 70 54

(a) Determine the least-squares regression line.

^

y =[]x +[] ( round to four decimal places as needed.)

Answer #1

The statistical software output for this problem is:

**Simple linear regression results:**

Dependent Variable: y

Independent Variable: x

y = 133 - 1.29 x

Sample size: 5

R (correlation coefficient) = -0.99787352

R-sq = 0.99575156

Estimate of error standard deviation: 1.5383974

**Parameter estimates:**

Parameter | Estimate | Std. Err. | Alternative | DF | T-Stat | P-value |
---|---|---|---|---|---|---|

Intercept | 133 | 2.0639767 | ≠ 0 | 3 | 64.438711 | <0.0001 |

Slope | -1.29 | 0.048648398 | ≠ 0 | 3 | -26.516803 | 0.0001 |

**Analysis of variance table for regression
model:**

Source | DF | SS | MS | F-stat | P-value |
---|---|---|---|---|---|

Model | 1 | 1664.1 | 1664.1 | 703.14085 | 0.0001 |

Error | 3 | 7.1 | 2.3666667 | ||

Total | 4 | 1671.2 |

Hence,

a) Regression line equation:

= (-**1.29**) x + **133**

b) Sum of Squared residuals = SSE = **7.1**

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the data is the numbers connected to the x and y lines
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