1. for women age 25–34 in the hanes5 sample, the relationship between height and income can be summarized as follows: average height ≈ 64 inches, sd ≈ 2.5 inches average income ≈ $21,000, sd ≈ $20,000, r ≈ 0.2 the slope of the regression equation is . the y-intercept is the predicted income for a woman who is 67 inches tall is . the predicted income for a woman who is 60 inches tall is . the rms error for these predictions is (round your answer to 2 digits).

Step-by-step explanation:

Data given and  previous concepts

represent the sample mean for the height

represent the sample deviation for the height

represent the sample mean for the income

represent the sample deviation for the income

r=0.2 represent the correlation coefficient

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

Solution to the problem

Let's suppose that we have the following linear model:

Where Y is the dependent variable (income) and X the independent variable (height). represent the intercept and the slope.  

In order to estimate the coefficients we can use least squares estimation.  

We have an useful formula in order to estimate the slope for the linear model given by:

Now we can find the intercept for the linear model with the following formula:

And then our linear model would be given by:

We can estimate the RMS with the following formula:

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