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-valueequals0.000, 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.

Step-by-step explanation:

Data given

n=20 represent the sampel size

represent the sample mean for the independent variable (IQ score of the husband)

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:

Where is the intercept and the slope

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

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:

On this case is the best predicted value because we have an unbiased estimator.

probability for j is 1/4

while

a is 1/6