Question

# How strongly do physical characteristics of sisters and brothers correlate? Here are data on the heights...

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?

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

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