latasha was presented with the following data set and argued that there was no correlation between x and y…

Answer:

LaTasha is correct.

Explanation:

Step1: Calculate the means

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

Step2: Calculate the slope $b$

$b=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})(y_i - \bar{y})}{\sum_{i=1}^{n}(x_i-\bar{x})^2}$ $\sum_{i = 1}^{7}(x_i - 4)(y_i-4.43)=(1 - 4)(4 - 4.43)+(2 - 4)(5 - 4.43)+(3 - 4)(4 - 4.43)+(4 - 4)(5 - 4.43)+(5 - 4)(4 - 4.43)+(6 - 4)(5 - 4.43)+(7 - 4)(4 - 4.43)$ $=(- 3)(-0.43)+(-2)(0.57)+(-1)(-0.43)+(0)(0.57)+(1)(-0.43)+(2)(0.57)+(3)(-0.43)$ $=1.29-1.14 + 0.43+0-0.43+1.14-1.29 = 0$ Since the numerator of the slope formula is 0, $b = 0$.

Step3: Analyze the correlation

A regression equation of the form $y=bx + a$ with $b = 0$ (in this case $y=a$) implies no linear - relationship between $x$ and $y$. So there is no correlation (linear correlation in this context) between $x$ and $y$.