Question

In a recent college statistics class, data was collected on each student's height and their shoe size. The first three tables of the regression output are below the conclusions.  Please agree or disagree with the conclusions and, of course, state your statistical reasoning.

1. There is sufficient evidence to believe that a statistically significant relationship exists between a student's height and his/her shoe size.
2. About 80% of the variation in shoe size is determined by the variation in height.
3. For each change in height of 0.3598 inches, the student’s shoe size changes by 1.

Regression Statistics
R		0.80638
R-Squared		0.65025
Adjusted R-Squared		0.63897
S		1.19
Sample Size		33
Regression equation: shoe size = - 15.08781 + (0.35978 * Height)
ANOVA
	d.f.	SS	MS	F	p-value
Regression	1.	81.61618	81.61618	57.63463	0
Residual	31.	43.89898	1.4161
Total	32.	125.51515
	Coefficient	Standard Error	LCL	UCL	t Stat	p-value
Intercept	-15.08781	3.19558	-21.60524	-8.57038	-4.72146	0.00005
Height	0.35978	0.04739	0.26313	0.45644	7.59175	0
Tcrit (5%)	2.03951

Answer 1

(A) I agree with this statement because the p value corresponding to slope coefficient of height is 0.000, which means that the slope coefficient is a significant estimator of the shoe size

therefore, we can say that there is sufficient evidence to believe that a statistically significant relationship exists between height and shoe size

(B) I disagree with this statement because the % of variation explained by independent variable in the dependent variable is given by the value of coefficient of determination

In this coefficient of determination is 0.639 or 63.9%, which means that only 63.9% variation is explained. So, the given statement is incorrect

(C) I disagree with this statement because the slope coefficient tells us about the change in dependent variable caused by the change in independent variable

Slope coefficient of height is 0.3598, which means that for every one unit change in height, shoe size will change by 0.3598

So, the given statement is incorrect