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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.

Respuesta :

Answer:

[tex]\hat y = -3.34+ 1.07(91) = 94.03[/tex]

Step-by-step explanation:

Data given

n=20 represent the sampel size

[tex]\bar X = 100.39[/tex] represent the sample mean for the independent variable (IQ score of the husband)

[tex]\bar y = 103.6[/tex] 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:

[tex]y = \beta_0 + \beta_1 x[/tex]

Where [tex]\beta_0[/tex] is the intercept and [tex]\beta_1[/tex] the slope

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

[tex]\hat y = -3.34 +1.07 x[/tex]

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:

[tex]\hat y = -3.34+ 1.07(91) = 94.03[/tex]

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

MrRoyal

The best predicted value for a husband with an IQ of 91 is 94.03

How to determine the model?

The given parameters are:

  • Sample size, n = 20
  • Mean of x = 100.39​
  • Mean of y = 103.6​
  • Correlation coefficient, r = 0.925
  • ​P-value ​= 0.000
  • Regression equation, y = -3.34 + 1.07x​

For a husband with an IQ of 91, the best predicted value is:

y = -3.34 + 1.07 * 91

Evaluate

y = 94.03

Hence, the best predicted value for a husband with an IQ of 91 is 94.03

Read more about regression equations at:

https://brainly.com/question/26755306

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