Question

suppose iq scores were obtained for 20 randomly selected sets of siblings. the 20 pairs of measurements yield \\( \bar{x} = 101.45 \\), \\( \bar{y} = 100.95 \\), \\( r = 0.939 \\), p - value = 0.000, and \\( \hat{y} = - 7.24 + 1.07x \\), where \\( x \\) represents the iq score of the younger child. find the best predicted value of \\( \hat{y} \\) given that the younger child has an iq of 105? use a significance level of 0.05. click the icon to view the critical values of the pearson correlation coefficient \\( r \\). the best predicted value of \\( \hat{y} \\) is \\( \square \\). (round to two decimal places as needed.)

Explanation:

Step1: Identify the regression equation

The given regression equation is $\hat{y} = -7.24 + 1.07x$, where $x$ is the IQ score of the younger child.

Step2: Substitute x = 105 into the equation

Substitute $x = 105$ into $\hat{y} = -7.24 + 1.07x$:
$\hat{y} = -7.24 + 1.07\times105$
First, calculate $1.07\times105 = 112.35$
Then, $\hat{y} = -7.24 + 112.35 = 105.11$

Answer:

105.11