Question

ch 5 if y is the response variable and x is the explanatory variable, what does the regression line allow you to do that correlation does not?

calculate the exact value of y given a value for x

calculate the exact value of x given a value for y

calculate the predicted value of x given a value for y

calculate the predicted value of y given a value for x

Explanation:

Correlation only measures the strength and direction of a linear relationship between two variables. A regression line, on the other hand, is used to model the relationship between a response variable \(y\) and an explanatory variable \(x\). It allows us to predict the value of \(y\) for a given \(x\) using the equation of the line \(y = a+bx\) (for simple linear regression), where \(a\) is the intercept and \(b\) is the slope. We do not calculate exact values (due to the presence of residual error in real - world data), and we are focused on predicting \(y\) (the response variable) from \(x\) (the explanatory variable) in the context of the regression line for \(y\) on \(x\).

Answer:

calculate the predicted value of \(y\) given a value for \(x\)