analyzing regression results\nlatasha was presented with the following data set and argued that there was no…

Explanation:

Step1: Calculate the means of x and y

$\bar{x}=\frac{1 + 2+3+4+5+6+7}{7}=\frac{28}{7} = 4$ $\bar{y}=\frac{4 + 5+4+5+4+5+4}{7}=\frac{31}{7}\approx4.43$

Step2: Calculate the slope (b) of the regression line

$b=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}$ $(x_1-\bar{x})(y_1 - \bar{y})=(1 - 4)(4-\frac{31}{7})=(- 3)\times(4-\frac{31}{7})=(-3)\times\frac{28 - 31}{7}=\frac{9}{7}$ $(x_2-\bar{x})(y_2 - \bar{y})=(2 - 4)(5-\frac{31}{7})=(-2)\times\frac{35 - 31}{7}=-\frac{8}{7}$ $(x_3-\bar{x})(y_3 - \bar{y})=(3 - 4)(4-\frac{31}{7})=(-1)\times\frac{28 - 31}{7}=\frac{3}{7}$ $(x_4-\bar{x})(y_4 - \bar{y})=(4 - 4)(5-\frac{31}{7})=0$ $(x_5-\bar{x})(y_5 - \bar{y})=(5 - 4)(4-\frac{31}{7})=(1)\times\frac{28 - 31}{7}=-\frac{3}{7}$ $(x_6-\bar{x})(y_6 - \bar{y})=(6 - 4)(5-\frac{31}{7})=(2)\times\frac{35 - 31}{7}=\frac{8}{7}$ $(x_7-\bar{x})(y_7 - \bar{y})=(7 - 4)(4-\frac{31}{7})=(3)\times\frac{28 - 31}{7}=-\frac{9}{7}$ $\sum_{i = 1}^{7}(x_{i}-\bar{x})(y_{i}-\bar{y})=\frac{9}{7}-\frac{8}{7}+\frac{3}{7}+0-\frac{3}{7}+\frac{8}{7}-\frac{9}{7}=0$ $(x_1-\bar{x})^2=(1 - 4)^2 = 9$ $(x_2-\bar{x})^2=(2 - 4)^2 = 4$ $(x_3-\bar{x})^2=(3 - 4)^2 = 1$ $(x_4-\bar{x})^2=(4 - 4)^2 = 0$ $(x_5-\bar{x})^2=(5 - 4)^2 = 1$ $(x_6-\bar{x})^2=(6 - 4)^2 = 4$ $(x_7-\bar{x})^2=(7 - 4)^2 = 9$ $\sum_{i = 1}^{7}(x_{i}-\bar{x})^{2}=9 + 4+1+0+1+4+9 = 28$ $b = 0$

Step3: Analyze the result

Since the slope of the regression line $b = 0$, there is no linear - relationship between $x$ and $y$. LaTasha is correct.

Answer:

LaTasha is correct because the slope of the regression line is 0, indicating no linear correlation between x and y.