AP Statistics

 Least Squares regression is a way of finding a line that summarizes the relationship between two variables.

 A regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes. We often use the regression line for predicting the value of y for a given value of x. The least squares regression line of y on x is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible

 In order to obtain the equation for the least squares regression line, we must first calculate the mean and standard deviation of both x and y denoted  The equation for the least squares regression line is the line  Where the slope b is  And the intercept a is

 Ralph has been studying the effect of time someone studies on time involved in extracurricular activities. The average time someone studies is 5.7 hours with standard deviation The average time involved in extracurricular activities is 7.9 hours with standard deviation If the correlation is r = -0.5, find the equation of the least squares regression line.

 Lets calculate the least squares regression line for the Sanchez family’s gas consumption. We drew the scatterplot in section 3.1. Here is the data and the scatterplot that we obtained.

 Make sure your diagnostics are on  Put your explanatory variable values into List 1 and your response variable values into list 2  STAT  CALC  Choose #8 LinReg a + bx  Enter