Question

SEX   AGE   FOOT LENGTH   SHOE PRINT   SHOE SIZE   HEIGHT
M   67   27.8   31.3   11.0   180.3
M   47   25.7   29.7   9.0   175.3
M   41   26.7   31.3   11.0   184.8
M   42   25.9   31.8   10.0   177.8
M   48   26.4   31.4   10.0   182.3
M   34   29.2   31.9   13.0   185.4
M   26   26.8   31.8   11.0   180.3
M   29   28.1   31.0   10.5   175.3
M   60   25.4   29.7   9.5   177.8
M   48   27.9   31.4   11.0   185.4
M   30   27.5   31.4   11.0   190.5
M   43   28.8   31.6   12.0   195.0
M   54   26.7   31.8   10.0   175.3
M   31   26.7   32.4   10.5   180.3
M   42   25.1   27.6   9.0   172.7
M   21   28.7   31.8   12.5   182.9
M   59   29.2   31.3   11.0   189.2
M   58   27.9   31.3   11.5   185.4
M   42   28.6   34.5   14.0   193.7
F   47   23.2   24.8   7.0   165.1
F   19   24.3   28.6   9.0   166.4
F   20   26.0   25.4   10.0   177.8
F   27   23.8   26.7   8.0   167.6
F   19   25.1   26.7   9.0   168.3
F   21   25.4   27.9   8.5   165.7
F   32   21.9   27.9   8.0   165.1
F   19   26.2   28.9   11.0   165.1
F   27   23.8   27.9   8.0   165.1
F   18   22.2   25.9   9.5   152.4
F   26   24.6   25.4   8.5   162.6
F   36   24.6   28.1   9.0   179.1
F   28   23.7   27.6   9.0   175.9
F   29   25.6   26.5   8.5   166.4
F   58   24.1   26.5   7.0   167.6
F   30   23.8   28.4   9.0   162.6
F   23   23.3   26.5   8.0   167.6
F   26   23.5   26.0   8.0   165.1
F   47   25.1   27.0   10.0   172.7
F   36   24.1   25.1   7.5   157.5
F   19   23.8   27.9   10.0   167.6

1.What is the value of the test statistic for the test of correlation?

2.What proportion of the variation in shoe sizes is explained by height?

3.What is the value of the sample correlation coefficient, written to three decimal places?

4.My cousin is 16 centimeters shorter than me. Based on the model, predict how many shoe sizes smaller his shoes are.

5.Predict what the average shoe size should be for someone that is 6 feet tall according to the model. Report your prediction out to one decimal place. (Hint - heights in the data set are in centimeters, so they are also in cm for the model!)

Answer 1

1.What is the value of the test statistic for the test of correlation?

t = 7.663

2.What proportion of the variation in shoe sizes is explained by height?

0.607

3.What is the value of the sample correlation coefficient, written to three decimal places?

r = 0.779

4.My cousin is 16 centimeters shorter than me. Based on the model, predict how many shoe sizes smaller his shoes are.

y = -11.9462 + 0.1245*x

Put x = 16

y = -11.9462 + 0.1245*16

y = -9.9542 = 10 shoe sizes smaller

5.Predict what the average shoe size should be for someone that is 6 feet tall according to the model. Report your prediction out to one decimal place. (Hint - heights in the data set are in centimeters, so they are also in cm for the model!)

y = -11.9462 + 0.1245*x

Put x = 182.88

y = -11.9462 + 0.1245*182.88 = 10.82236

	r²	0.607
	r	0.779
	Std. Error	1.022
	n	40
	k	1
	Dep. Var.	SHOE SIZE
ANOVA table
Source	SS	df	MS	F	p-value
Regression	61.3206	1	61.3206	58.73	3.17E-09
Residual	39.6794	38	1.0442
Total	101.0000	39
Regression output				confidence interval
variables	coefficients	std. error	t (df=38)	p-value	95% lower	95% upper
Intercept	-11.9462
HEIGHT	0.1245	0.0162	7.663	3.17E-09	0.0916	0.1573

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