psychologist has collected data on the number of times x
per year a college student goes out on a date and the number of hours y of homework that student does per week. She came
up with the equation of the regression line
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This is what she does to come up withe the regression line:
She first calculates the following
The mean of the x values
The mean of the y values
The standard deviation of the x values (denoted sx)
The standard deviation of the y values (denoted sy)
The correlation between X and Y (denoted r)
The formula for the slope, m, of the best-fitting line is
where r is the correlation between X and Y, and sx and sy are the standard deviations of the x-values and the y-values, respectively. You simply divide syby sx and multiply the result by r.
She then finds the y intercept using the formula below
are the means of the x-values and the y-values, respectively, and m is the slope.
So to calculate the y-intercept, b, of the best-fitting line, you start by finding the slope, m, of the best-fitting line using the above steps. Then to find the y-intercept, you multiply m by
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