Question

Data on which regression calculations were found:

Student	Height	shoe size
1	63	7.5
2	75	13
3	62	9
4	62	6
5	71	9.5
6	69	7.5
7	72	10
8	69	10
9	64	9.5
10	73	12
11	69	8.5
12	68	10
13	63	9
14	62	7
15	64	6
16	66	9
17	70	10
18	71	9
19	62	7
20	66	7
21	76	12
22	65	10.5
23	64	7.5
24	72	11
25	63	8
26	73	11
27	65.5	10
28	62	6
29	69	12
30	66	8
31	76	13
32	64	7.5
33	64	8

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 insufficient 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

Answer 1

Answer

Data table is given for the regression analysis between Shoe size and individual height

ANOVA data table shows that the result is significant because the F statistic is 57.63 with p value less than 0.001. This tells us that there must be a significant correlation between the dependent and independent variable

R square value is 65.03%, which means that 65.03% variation in the shoe size of an individual can be explained by height.

Slope coefficient for height is 0.3599 with t statistic 7.59 and p value less than 0.001. P value is significant because it is less than significance level of 0.05

Therefore, overall results show that there is a significant linear relationship between the shoe size and height

First statement is incorrect because we have sufficient evidence to show that there is a significant relationship between shoe size and height

Second statement is correct because correlation is positive and slope is also positive, which means that there is a significant positive relationship

third statement is incorrect because slope of height is 0.3599, but not 15