Practice Linear Regression in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Linear regression is a statistical method for modeling the relationship between a dependent variable and one or more independent variables by fitting a straight line that minimizes the sum of squared distances from data points to the line (least squares method).

Given scattered points, draw the 'best' line through them. 'Best' means the line that's closest to all points on average. This line lets you predict Y from X.

Example 1

hard
A regression line is \hat{y} = 2.5 + 1.8x, where x is hours studied and \hat{y} is predicted exam score. Interpret the slope and y-intercept.

Example 2

hard
Using \hat{y} = 10 + 3x, predict y when x = 5. Is it appropriate to predict for x = 50 if the data ranged from x = 1 to x = 10?

Example 3

hard
A regression equation is \hat{y} = 50 - 2.3x. Interpret the slope. If x = 8, find \hat{y}.

Example 4

hard
A regression line is \hat{y} = 4 + 1.5x. Predict y when x = 12, and decide whether this is interpolation if the observed x-values ranged from 5 to 15.
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