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

analyzing regression results\nlatasha was presented with the following data set and argued that there was no correlation between x and y. is latasha correct? use the regression equation to explain your reasoning\nx 1 2 3 4 5 6 7\ny 4 5 4 5 4 5 4

analyzing regression results\nlatasha was presented with the following data set and argued that there was no correlation between x and y. is latasha correct? use the regression equation to explain your reasoning\nx 1 2 3 4 5 6 7\ny 4 5 4 5 4 5 4

Answer

Explanation:

Step1: Calculate means of x and y

$\bar{x} = \frac{1+2+3+4+5+6+7}{7} = 4$, $\bar{y} = \frac{4+5+4+5+4+5+4}{7} \approx 4.4286$

Step2: Compute slope of regression line

$b_1 = \frac{n\sum(xy)-(\sum x)(\sum y)}{n\sum x^2-(\sum x)^2}$. $\sum(xy)=124$, $n\sum(xy)=7124=868$, $(\sum x)(\sum y)=2831=868$. Numerator=0, so $b_1=0$.

Answer:

LaTasha is correct. The regression slope is 0, indicating no linear correlation between x and y.