The Regression Equation

We know that the regression equation is $y = a + bx$, where y is the variable you are predicting, a is the intercept (the value of the response variable when the predictor is 0) and b is the slope. We can calculate the value of b with the following equation: $$b = r \frac{sd_y} {sd_x}$$. Remember that x is the predictor variable and y is the response variable, and $r$ is the correlation between the two.

We're going to have a go at manually calculating the value of the slope in our money and liking study!

To do this you'll need to use two functions: cor() and sd(). cor() is used to caculate a correlation coefficient, and takes the two variables you are interested in as its first arguments. For example: cor(variable1, variable2). sd() calculates the standard deviation of given data, and takes the name of your data object as its first argument. For example: sd(variable1). Let's put these to use in your script!

Add code your script to assign the correlation between liking and money to cxy.
Add code to your script to assign the standard deviation of money to sx.
Add code to your script to assign the standard deviation of liking to sy.
In your script, use cxy, sx and sy to calculate the slope using the slope equation.

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Exercise

The Regression Equation

Instructions