Suppose IQ scores were obtained from randomly selected siblings For 20 such pair

Question

Suppose IQ scores were obtained from randomly selected siblings For 20 such pairs of people, the linear correlation coefficient is 0.896 and the equation of the regression line is y = -5.04 + 1.04x, where x represents the IQ score of the younger child. Also, the 20 x values have a mean of 95.31 and the 20 y values have a mean of 94.15. What is the best predicted IQ of the older child, given that the younger child has an IQ of 101? Use a significance level of 0.06. The best predicted IQ of the older child is.

Explanation / Answer

Here we have n= 20 and r = 0.896

Degree of freedom of t test: df =n-2 = 18

From table critical value of Pearson's coefficient is 0.468. Since r is greater than critical value so there is significant relationship between the variables. That is we can use regression line for pediction.

The best predicted value for X= 101 is

y' = -5.04 + 1.04x = -5.04 + 1.04*101 = 100

hence, best predicted IQ of the older child is 100.00.

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