Question

Enter the Shoe Size and Height data from the In class data Excel file (use the excel in class data lab file loaded into the files section of Canvas) into the week 7 Regression Excel sheet. Create a scatter plot for the data, store and graph the regression equation, and note the r² and r value.

1. Looking at the graph and the r, and r^2 value, do you feel that shoe size is a good predictor for height? Explain your reasoning for each.
2. Assuming that shoe size is a good predictor, what would the estimated height be for someone who wears size 10 shoes? Either show work or explain how your answer was calculated.
3. Do you think that organizing the data by gender would make a difference in how well shoe size predicts height? Are women’s shoe sizes the same as men’s? Is this a factor that should also be considered? Explain. (A great explanation would provide evidence supporting the conclusions. A good explanation can simply use reason.)

Shoe Size	Height (inches)
10	61
5	62
6	63
12	63
8	64
8	65
9	65
10	66
7	66
11	67
10	67
7	67
9	67
11	68
10	68
12	69
11	69
13	69
9	69
11	69
8	69
9	69
9	70
5	70
10	70
12	70
9	70
11	71
9	71
10	71
9	73
9	73
7	74
11	74
13	75

Answer 1

I used R software to solve this problem.

R code:

> size=scan('clipboard')
Read 35 items
> size
[1] 10 5 6 12 8 8 9 10 7 11 10 7 9 11 10 12 11 13 9 11 8 9 9 5 10
[26] 12 9 11 9 10 9 9 7 11 13
> height=scan('clipboard')
Read 35 items
> height
[1] 61 62 63 63 64 65 65 66 66 67 67 67 67 68 68 69 69 69 69 69 69 69 70 70 70
[26] 70 70 71 71 71 73 73 74 74 75
> fit=lm(height~size)
> summary(fit)

Call:
lm(formula = height ~ size)

Residuals:
Min 1Q Median 3Q Max
-7.6722 -1.9103 -0.1485 1.8278 6.7567

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 63.9093 2.7372 23.348 <2e-16 ***
size 0.4763 0.2841 1.677 0.103
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.344 on 33 degrees of freedom
Multiple R-squared: 0.07851, Adjusted R-squared: 0.05059
F-statistic: 2.812 on 1 and 33 DF, p-value: 0.103

> plot(height~size) # it gives scatter plot
> abline(fit) # it plot regression line on scatter plot

Scatter plot: