Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Sep 25, 2023

Find the best predicted IQ score $\hat{y}$ for a wife given her husband's IQ of $97$ , using a significance level of $0.05$ , where $\bar{x}=101.08$ , $\bar{y}=101.25$ , $r=0.825$ , and $\hat{y}=10.2+0.9x$ .

STEP 1

Assumptions1. The sample size is20 couples. . The mean IQ score of the husbands is $\bar{x}=101.08$ .
3. The mean IQ score of the wives is $\bar{y}=101.25$ .
4. The correlation coefficient is $r=0.825$ .
5. The-value is $0.000$ .
6. The regression equation is $\hat{y}=10.+0.9x$ .
7. We are asked to predict the wife's IQ score given that the husband's IQ score is $97$ .
8. The significance level is $0.05$ .

STEP 2

We have the regression equation $\hat{y}=10.2+0.9x$ , where $x$ is the husband's IQ score and $\hat{y}$ is the predicted wife's IQ score.

STEP 3

We are asked to find the best predicted value of $\hat{y}$ given that the husband's IQ score is $97$ . We can do this by substituting $x=97$ into the regression equation.
$\hat{y}=10.2+0.9(97)$

STEP 4

Calculate the value of $\hat{y}$ .
$\hat{y}=10.2+0.9(97) =97.$ The best predicted value of $\hat{y}$ is $97.$ .

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