Question

analyzing regression results
latasha 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
x 1 2 3 4 5 6 7
y 4 5 4 5 4 5 4

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

$b_1 = \frac{n\sum(xy)-(\sum x)(\sum y)}{n\sum x^2-(\sum x)^2}$. $\sum(xy)=124$, $n\sum(xy)=7*124=868$, $(\sum x)(\sum y)=28*31=868$. Numerator=0, so $b_1=0$.

Answer:

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