Question

How strongly do physical characteristics of sisters and brothers correlate? Here are data on the heights (in inches) of 12 adult pairs:

Brother 71 68 66 67 70 71 70 73 72 65 66 70

  Sister 69 64 65 63 65 62 65 64 66 59 62 64

a. Use your calculator or software to find the correlation and the equation of the least-squares line for predicting sister’s height from brother’s height. Make a scatterplot of the data, and add the regression line to your plot.

b. Damien is 70 inches tall. Predict the height of his sister Tonya. Based on the scatterplot and the correlation r, do you expect your prediction to be very accurate? Why?

Answer 1

x= Brother , y= sister

x	y	xy	x2	y2
71	69	4899	5041	4761
68	64	4352	4624	4096
66	65	4290	4356	4225
67	63	4221	4489	3969
70	65	4550	4900	4225
71	62	4402	5041	3844
70	65	4550	4900	4225
73	64	4672	5329	4096
72	66	4752	5184	4356
65	59	3835	4225	3481
66	62	4092	4356	3844
70	64	4480	4900	4096
829	768	53095	57345	49218	Total
69.08333	64				Average

Correlation(r) = 0.55463 (use Excel function =Correl(xarray, yarray) i.e =correl(A2:A13,B2:B13))

Y= 0.5206x + 28.037

b) x = 70

Y= 0.5206*70 + 28.037 = 64.479.

It is not very accurate because of r, the value of r is <0.7 which show not highly correlated