Quantitative Analysis for Management, 13/e

Key Equations

(4-1)

$$Y={\beta }_0+{\beta }_{1}X+P$$

Underlying linear model for simple linear regression.

(4-2)

$$\widehat{Y}=b_0+b_{1}X$$

Simple linear regression model computed from a sample.

(4-3)

$$e=Y-\widehat{Y}$$

Error in regression model.

(4-4)

$$b_1=\frac{\sum \left(X-\overline{X}\right)\left(Y-\overline{Y}\right)}{\sum {\left(X-\overline{X}\right)}^2}$$

Slope in the regression line.

(4-5)

$$b_0=\overline{Y}-b_1\overline{X}$$

Intercept in the regression line.

(4-6)

$$\text{SST = }\Sigma {\text{(}Y\text{ - }\overline{Y}\text{)}}^{\text{2}}$$

Total sums of squares.

(4-7)

$$\text{SSE = }\Sigma e^2\text{=}\Sigma {\text{(}Y\text{ - }\widehat{Y}\text{)}}^{\text{2}}$$

Sum of squares due to error.

(4-8)

$$\text{SSR}=\Sigma {\left(\widehat{Y}-\overline{Y}\right)}^2$$

Sum of squares due to regression.

(4-9)

$$\text{SST}=\text{SSR}+\text{SSE}$$

Relationship among sums of squares in regression.

(4-10)

$$r^2=\frac{\text{SSR}}{\text{SST}}=1-\frac{\text{SSE}}{\text{SST}}$$

Coefficient of determination.

(4-11)

$$r=\pm \sqrt{r^2}$$

Coefficient of correlation. This has the same sign as the slope.

(4-12)

$$s^2=\text{MSE}=\frac{\text{SSE}}{n-k-1}$$

An estimate of the variance of the errors in regression; ...