In a recent college statistics class, data was collected on each student's height and shoe size. The first three tables of the regression output with LOS = 0.05 are below the conclusions. Please agree or disagree with the conclusions and, of course, state your statistical reasoning.

1. There is not enough evidence to believe a statistically significant relationship exists between a student's height and his/her shoe size.
2. There is a strong, positive correlation between shoe size and height.
3. For each change in height of 15 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