Question

A random sample of 8 applicants for a certain foreign job is selected. The number of years that these applicants have studied French in high school or university, X, and the mark which they obtained in a proficiency test in French, Y, are recorded. The following information is given: ∑X =32 ∑Y =528 ∑XY=2136 ∑X² =130 ∑Y² =34872 Fitting a regression line, which of the following statements is incorrect

Answer 1

$n=8 \\ \sum X=32 \\ \sum Y=528 \\ \sum XY=2136 \\ \sum X^2= 130 \\ \sum Y^2= 34872 \\ \bar{X}= \frac{1}{n} \sum^8_{i=1}X_i = \frac{32}{8} = 4 \\ \bar{Y}= \frac{1}{n} \sum^8_{i=1}Y_i = \frac{528}{8} = 66 \\ SS_{XX}= \sum^n_{i=1} X^2 -\frac{1}{n}(\sum^n_{i=1}X_i)^2 = 130 - \frac{1}{8}(32)^2 \\ = 130-128 =2 \\ SS_{YY} = \sum^n_{i=1} Y^2 -\frac{1}{n}(\sum^n_{i=1}Y_i)^2 = 34872 - \frac{1}{8}(528)^2 \\ =34872 -34848 = 24 \\ SS_{XY} = sum^n_{i=1} X_iY_i -\frac{1}{n}(\sum^n_{i=1}X_i)(\sum^n_{i=1}Y_i) \\ =2136 - \frac{1}{8}(32)(528) \\ = 2136-2112 =24 \\ Slope = m = \frac{SS_{XY}}{SS_{XX}}= \frac{24}{2}=12 \\ Intercept = n = \bar{Y} -\bar{X} \times m \\ = 66 -4 \times 12 \\ = 66-48 \\ = 18$

The regression equation:

Y=18+12X