Answer:
a) r = 0.13194
b) There is weak positive relationship between X and Y.
c) Slope ([tex]\beta}[/tex]) = 34.8333
d) Intercept ([tex]\alpha)[/tex] = -132.333
e) y = -132.33 + 34.83 x
f) the predicted sales of tires be if he spends five thousand dollars in advertising = 41.82 - (in thousands of tires)
Step-by-step explanation:
a) By the coefficient of determination, the formula is:
r = [tex]\frac{n\sum{x}\sum{y} - \sum{xy}}{\sqrt{(n\sum{x}^2 - (\sum{x})^2) (n\sum{y}^2 - (\sum{y})^2})}[/tex],
n = 6. Other values are provided too. Just substitute and obtain the value of r.
b) For correlation interpretation:
-1 ≤ r ≤ 1,
The closer the value to 1 the strong the relationship. If close to -1, there is strong negative relations and if close to +1, there is strong positive relationship. when the value is close to 0, there is weak positive relationship.
c) Slope is given as:
[tex]\beta = \frac{n\sum{x}\sum{y} - \sum{xy}}{n\sum{x}^2 - (\sum{x})^2 }[/tex], and
d) Intercept is given as:
[tex]\alpha = \bar{y} - \beta \bar{x}, \\\bar{y} = \frac{\sum{y}}{n} \; and, \; \bar{x} = \frac{\sum{x}}{n}[/tex]
e) We obtain [tex]\beta = 34.8333 \; and \; \alpha = -132.333[/tex], therefore, the estimated Regression equation:
y = -132.33 + 34.83 x
f) Since the values are given is thousands of dollar. Then 5000 dollars is simply 5. We substitute the value into x in the regression equation and we have:
y = -132.33 + 34.83*(5) = 41.82
