How strongly do physical characteristics of sisters and brothers correlate? Here

Question

How strongly do physical characteristics of sisters and brothers correlate? Here are data on the heights (in inches) of 11 adult pairs. Brother 71 7067 64 70 71 70 73 72 65 66 Sister 69 64 65 63 65 62 65 64 66 59 62 (a) Use your calculator or software to find the correlation. (Round your answer to three decimal places.) Give the least-squares line for predicting sister's height from brother's height. (Round your answer to three decimal places.) Make a scatterplot that includes this line. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Damien is 71 inches tall. Predict the height of his sister Tonya. (Round your answer to one decimal place.) nches Based on the scatterplot and the correlation r, do you expect your prediction to be very accurate? Why? (Select all that apply.) We should not place too much confidence in this prediction. There is very little variation about the line in the scatterplot. There is a lot of variation about the line in the scatterplot. There is no variation about the line in the scatterplot. We should place a lot of confidence in this prediction. The correlation is high The correlation is low

Explanation / Answer

Solution:

Suppose x: Sister’s height and y : Brother’s height

Using MINITAB,

a)Pearson correlation of x and y = 0.558

P-Value = 0.074

The regression equation is

y = 27.3 + 0.652 x

b) Here p-value (0.074) which is greater than 0.05 hence we can say that there is significant correlation between x and y.

Therefore, if x = 71 then y = 27.3 + 0.652*71 = 73.6

c) There is no perfect correlation but correlation seems average.

Also scatter plot shows high variation between x and y.

Hence we are not too much confident on predition.

Done

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