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

Answer:

LaTasha is incorrect. There is a correlation.

Explanation:

Step1: Calculate the means

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

Step2: Calculate the slope ($m$)

$m=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})(y_i - \bar{y})}{\sum_{i=1}^{n}(x_i-\bar{x})^2}$ $\sum_{i = 1}^{7}(x_i - 4)(y_i-4.4286)=(1 - 4)(4 - 4.4286)+(2 - 4)(5 - 4.4286)+(3 - 4)(4 - 4.4286)+(4 - 4)(5 - 4.4286)+(5 - 4)(4 - 4.4286)+(6 - 4)(5 - 4.4286)+(7 - 4)(4 - 4.4286)$ $=(- 3)(-0.4286)+(-2)(0.5714)+(-1)(-0.4286)+(0)(0.5714)+(1)(-0.4286)+(2)(0.5714)+(3)(-0.4286)$ $=1.2858-1.1428 + 0.4286+0 - 0.4286+1.1428-1.2858 = 0$ $\sum_{i=1}^{7}(x_i - 4)^2=(1 - 4)^2+(2 - 4)^2+(3 - 4)^2+(4 - 4)^2+(5 - 4)^2+(6 - 4)^2+(7 - 4)^2$ $=9 + 4+1+0+1+4+9 = 28$ $m = 0$

Step3: Calculate the y - intercept ($b$)

$b=\bar{y}-m\bar{x}=4.4286-0\times4 = 4.4286$ The regression equation is $y = 4.4286$. Although the slope is 0, the fact that we can find a non - trivial regression equation indicates a relationship (in this case, a horizontal relationship where $y$ has a constant expected value). So there is a correlation (a non - linear, constant relationship), and LaTasha is incorrect.