SOLUTION: Can someone please help? Suppose IQ scores were obtained from randomly selected twins. For 20 such pairs of​ people, the linear correlation coefficient is 0.793 and the eq

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Question 1011985: Can someone please help?
Suppose IQ scores were obtained from randomly selected twins. For 20 such pairs of​ people, the linear correlation coefficient is 0.793 and the equation of the regression line is ModifyingAbove y with caret equals 24.46 plus 0.75 xy=24.46+0.75x​, where x represents the IQ score of the twin born first twin born first. ​Also, the 20 x values have a mean of 106.43 and the 20 y values have a mean of 103.9. What is the best predicted IQ of the twin born second twin born second​, given that the twin born first twin born first has an IQ of 106? Use a significance level of 0.05.

The best predicted IQ of the twin born second twin born second is ___?
​(Round to two decimal places as​ needed.)
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
Can someone please help?
Suppose IQ scores were obtained from randomly selected twins. For 20 such pairs of​ people, the linear correlation coefficient is 0.793 and the equation of the regression line is ModifyingAbove y with caret equals 24.46 plus 0.75 xy=24.46+0.75x​, where x represents the IQ score of the twin born first twin born first. ​Also, the 20 x values have a mean of 106.43 and the 20 y values have a mean of 103.9. What is the best predicted IQ of the twin born second twin born second​, given that the twin born first twin born first has an IQ of 106? Use a significance level of 0.05.
The best predicted IQ of the twin born second twin born second is ___?
​(Round to two decimal places as​ needed.)
I'll get you started on this.

1) Calculate the critical t-value (groups consist of < 30 members) 

2) If the absolute value of the linear correlation coefficient (r) is > the critical t-value, a LINEAR CORRELATION EXISTS between

   the 2 groups (younger and older twins) of IQs. Thus, the regression equation: ŷ, or  can be used to predict

   the IQ of the younger twins (twins born second), by substituting the x-value 106 into the equation.

3) However, if  the absolute value of the linear correlation coefficient (r) is ≤ the critical t-value, a LINEAR CORRELATION DOES NOT

   exist between the 2 groups (younger and older twins) of IQs. Thus, the best predictor of y-hat or the younger twins' IQ is y: 

   the mean of the group: twin born second, or the younger twins (103.9) 

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