A student wonders if people of similar heights tend to date each other. She measures herself,...

A student wonders if people of similar heights tend to date each other. She measures herself, her roommate and the women in the adjoining rooms; then she measures the next man each woman dates. Here are the data (in inches):

Women	66	64	66	65	70	65	60	70	72	63
Men	72	68	70	68	71	65	64	66	70	69

A. What is the least squares regression line of the male height on female height? Graph it on a scatterplot. Make sure all parts are appropriately labeled.

B. Use your results from a. to predict the height of Jill’s next date if she is 68 inches tall.

C. What is the correlation of the data? What does the correlation describe?

D. Are there any influential outliers in the data set?

Solutions

Expert Solution

Women, X	Men, Y	XY	X²	Y²
66	72	4752	4356	5184
64	68	4352	4096	4624
66	70	4620	4356	4900
65	68	4420	4225	4624
70	71	4970	4900	5041
65	65	4225	4225	4225
60	64	3840	3600	4096
70	66	4620	4900	4356
72	70	5040	5184	4900
63	69	4347	3969	4761
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
661	683	45186	43811	46711

Sample size, n =	10
x̅ = Ʃx/n = 661/10 =	66.1
y̅ = Ʃy/n = 683/10 =	68.3

SSxx = Ʃx² - (Ʃx)²/n = 43811 - (661)²/10 =	118.9
SSyy = Ʃy² - (Ʃy)²/n = 46711 - (683)²/10 =	62.1
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 45186 - (661)(683)/10 =	39.7

A) Slope, b = SSxy/SSxx = 39.7/118.9 = 0.33389403

y-intercept, a = y̅ -b* x̅ = 68.3 - (0.33389)*66.1 = 46.2296047

Least squares regression line:

ŷ = 46.2296 + (0.3339) x

Scatterplot:

B) Predicted value of y at x = 68

ŷ = 46.2296 + (0.3339) * 68 = 68.93 cm

C) Correlation coefficient, r = SSxy/√(SSxx*SSyy) = 39.7/√(118.9*62.1) = 0.4620

The correlation describe that there is a weak positive relationship between women's height and men's height.

D) Yes, there are influential outliers in the data set.

orchestra answered 9 months ago

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