Question

1. The following information is from a sample of 15 women. They recorded the women’s weight in pounds and height in inches. You can use R to answer all of these questions, no need to do by hand.

Height	58	58	59	61	61	63	64	65	67	67	67	70	72	72	72
Weight	117	117	120	123	123	139	142	142	146	146	150	150	150	154	164

1. Draw a scatterplot of the data. Describe the relationship between height and weight.
2. Determine the covariance and correlation coefficient (r) between height and weight. Give the interpretation of the correlation.
3. Suppose we want to predict the weight of a women based on the height. Give the least-squares equation to predict weight based on height.

Answer 1

Height, X	Weight, Y	XY	X²	Y²
58	117	6786	3364	13689
58	117	6786	3364	13689
59	120	7080	3481	14400
61	123	7503	3721	15129
61	123	7503	3721	15129
63	139	8757	3969	19321
64	142	9088	4096	20164
65	142	9230	4225	20164
67	146	9782	4489	21316
67	146	9782	4489	21316
67	150	10050	4489	22500
70	150	10500	4900	22500
72	150	10800	5184	22500
72	154	11088	5184	23716
72	164	11808	5184	26896
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
976	2083	136543	63860	292429

Sample size, n =	15
x̅ = Ʃx/n = 976/15 =	65.0666667
y̅ = Ʃy/n = 2083/15 =	138.866667
SSxx = Ʃx² - (Ʃx)²/n = 63860 - (976)²/15 =	354.933333
SSyy = Ʃy² - (Ʃy)²/n = 292429 - (2083)²/15 =	3169.73333
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 136543 - (976)(2083)/15 =	1009.13333

a) Scatterplot:

There is a positive relationship between Height and weight.

b) Correlation coefficient, r = SSxy/√(SSxx*SSyy) = 1009.13333/√(354.93333*3169.73333) = 0.9514

There is a positive and strong correlation between height and weight. As height increases weight increases.

c) Slope, b = SSxy/SSxx = 2.84316304

y-intercept, a = y̅ -b* x̅ = -46.1284748

Regression equation :

ŷ = -46.1285 + (2.8432) x