Please Help me understand how to work this problem. I have been working on this problem for several days and do not understand what to do.
Suppose IQ scores were obtained from randomly selected twins. For 20 such pairs, of people the linear correlation coefficient is 0.922 and the equation of the regression line is ^y=10.82+.88x Where x represents the IQ score of the husband. Also the 20x values have a mean of 99.53 and the 20 y values have a mean of 98.3. What is the best predicted IQ of the twins, given that the twin born first has an IQ of 107. Use a significance level of 0.05. The best predicted IQ for the twin born second is _________(round to one decimal place as needed)
To solve this problem, we need to use the equation of the regression line: ^y = 10.82 + 0.88x.
In this equation, ^y represents the predicted IQ score for the given value of x, which represents the IQ score of the husband. We are given that the twin born first has an IQ score of 107.
To find the predicted IQ of the twin born second, we need to substitute the given x value into the regression equation. So, let's substitute x = 107 into the equation:
^y = 10.82 + 0.88(107)
= 10.82 + 94.16
= 104.98
Therefore, the best predicted IQ of the twins, given that the twin born first has an IQ of 107, is approximately 105.0.
Please note that in this problem, the correlation coefficient and regression line equation are given as part of the problem statement. In real-life scenarios, you would typically need to calculate these values using statistical methods.