Question

"Correlation/Regression QB"

A researcher wants to determine the relationship between Father’s IQ (X) and Son’s IQ (Y). The researcher selects 16 fathers and measures their IQ and one of each of their son’s IQ. The data are presented below.
Father’s IQ: 144,   136,   132,   125,   119,   117,   115,   112,   108,   101,   98,    97,   91,   90,   88,   87
Son’s IQ:      134,   142,   122,   130,   115,   117,   110,     95,   112,   100,   83, 106,   87,   89,   89,   97

10) If appropriate, calculate the proportion of variation in Son's IQ that is not accounted for by Father's IQ (Round to two decimal places). If it is not appropriate to calculate this, input 999. 11) If appropriate, calculate the slope of the regression equation for predicting Son's IQ from Father's IQ (Round to three decimal places). If it is not appropriate to calculate, input 999.

12) If appropriate, calculate the y-intercept of the regression equation for predicting Son's IQ from Father's IQ (Round to three decimal places). If it is not appropriate to calculate, input 999. 13) If appropriate to calculate, what would you predict for the Son's IQ of a Father who had an IQ of 140 (Round to three decimal places)? If not appropriate to calculate, input 999.

Answer 1

we will run the regression analysis in excel

10)

19% of the variation in Son's IQ is not accounted for by Father's IQ

11)

the slope of the regression equation for predicting Son's IQ from Father's IQ is 0.894

12)

the y-intercept of the regression equation for predicting Son's IQ from Father's IQ = 9.650

Son's IQ of a Father who had an IQ of 140 is 9.650+0.894*140 = 134.81