Question

Suppose IQ scores were obtained for 20 randomly selected sets of couples. The 20 pairs of measurements yield x overbarequals100.39​, y overbarequals103.6​, requals0.925​, ​P-valueequals​0.000, and ModifyingAbove y with caret equals negative 3.34 plus 1.07 x​, where x represents the IQ score of the husband. Find the best predicted value of ModifyingAbove y with caret given that the husband has an IQ of 91​? Use a significance level of 0.05.

Answer 1

Answer:

$\hat y = -3.34+ 1.07(91) = 94.03$

Step-by-step explanation:

Data given

n=20 represent the sampel size

$\bar X = 100.39$ represent the sample mean for the independent variable (IQ score of the husband)

$\bar y = 103.6$ represent the sample mean for the dependent variable.

r =0.925 represent the correlation coefficient

Solution to the problem

The general expression for a linear model is given by:

$y = \beta_0 + \beta_1 x$

Where $\beta_0$ is the intercept and $\beta_1$ the slope

For this case we have a linear model given by the following expression:

$\hat y = -3.34 +1.07 x$

Where -3.34 is the intercept and 1.07 the slope. In order to find the best predicted value when X = 91 we just need to replace into the equation the value of 91 and we got this:

$\hat y = -3.34+ 1.07(91) = 94.03$

On this case is the best predicted value because $E(\hat y) = y$ we have an unbiased estimator.