Answer to Question #346246 in Statistics and Probability for wiwili

Question

In a biology class, a group of students brought 9 mice for their experiment. They measured the weight and the length of the body of each mouse from the tail to the nose. The findings are recorded below:

Length in cm

13

14

14

11

12

13

12

14

14

Weight in kg

10

10

12

11

16

14

14

17

17

What is the slope of the regression equation? Round your answers to the nearest hundredths.

Answer 1

In order to compute the regression coefficients, the following table needs to be used:

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c:c} & X & Y & XY & X^2 & Y^2 \\ \hline & 13 & 10 & 130 & 169 & 100 \\ \hdashline & 14 & 10 & 140 & 196 & 100 \\ \hdashline & 14 & 12 & 168 & 196 & 144 \\ \hdashline & 11 & 11 & 121 & 121 & 121 \\ \hdashline & 12 & 16 & 192 & 144 & 256 \\ \hdashline & 13 & 14 & 182 & 169 & 196 \\ \hdashline & 12 & 14 & 168 & 144 & 196 \\ \hdashline & 14 & 17 & 238 & 196 & 289 \\ \hdashline & 14 & 17 & 238 & 196 & 289 \\ \hdashline Sum= & 117 & 121 & 1577 & 1531 & 1691 \\ \hdashline \end{array}$$ $$\bar{X}=\dfrac{1}{n}\sum _{i}X_i=\dfrac{117}{9}=13$$

$$\bar{Y}=\dfrac{1}{n}\sum _{i}Y_i=\dfrac{121}{9}=13.44$$

$$SS_{XX}=\sum_iX_i^2-\dfrac{1}{n}(\sum _{i}X_i)^2$$ $$=1531-\dfrac{117^2}{9}=10$$

$$SS_{YY}=\sum_iY_i^2-\dfrac{1}{n}(\sum _{i}Y_i)^2$$ $$=1691-\dfrac{121^2}{9}=64.22$$

$$SS_{XY}=\sum_iX_iY_i-\dfrac{1}{n}(\sum _{i}X_i)(\sum _{i}Y_i)$$ $$=1577-\dfrac{117(121)}{9}=4$$

$$slope=b=\dfrac{SS_{XY}}{SS_{XX}}=\dfrac{4}{10}=0.40$$

$$a=\dfrac{121}{9}-0.4(13)=8.24$$

The regression equation is:

$$Y=8.24+0.40X$$