Suppose IQ scores were obtained for 20 randomly selected sets of couples. The 20 pairs of measurements yield x=97.47​, y=97.35​, r=0.892​, ​ P=0.000, and y=-9.15+1.09x​, where x represents the IQ score of the wife. Find the best predicted value of y given that the wife has an IQ of 104​ ? Use a significance level of 0.05.

Question:

Suppose IQ scores were obtained for 20 randomly selected sets of couples. The 20 pairs of measurements yield x' = 97.47, y' = 97.35, r=0.892, P=0.000, and y^=-9.15+1.09x, where x represents the IQ score of the wife. Find the best predicted value of y given that the wife has an IQ of 104? Use a significance level of 0.05.

Answer:

y^ = 104.21

Step-by-step explanation:

Given:

n = 20

x' = 97.47

y' = 97.35

r = 0.892

P-value = 0.000

y^ = - 9.15 + 1.09x

Here, the wife has an IQ of 104.

The regression equation here is given as:

y^ = - 9.15 + 1.09x

Let x represent the IQ of the wife.

x = 104

Hence, the best predicted value of y^ will be:

Let's substitute 104 for x in tge regression equation.

y^ = - 9.15 + 1.09 (104)

y^ = - 9.15 + 113.36

y^ = 104.21

Therefore, the best predicted value of y^ = 104.21