Stats Lsrl

How does the least squares regression line minimize the sum of squared residuals?

• By finding the line that has the smallest sum of the squared vertical distances between the observed data points and the predicted values on the line.

• By finding the line that has the smallest sum of the squared horizontal distances between the observed data points and the predicted values on the line.

• By finding the line that has the largest sum of the squared vertical distances between the observed data points and the predicted values on the line.

• By finding the line that has the smallest sum of the absolute vertical distances between the observed data points and the predicted values on the line.

How do you interpret the coefficient of determination in least squares regression?

• The coefficient of determination represents the correlation between the explanatory and response variables.

• The coefficient of determination represents the proportion of the variance in the response variable that can be explained by the explanatory variable(s).

• The coefficient of determination represents the average of the explanatory and response variables.

• The coefficient of determination represents the proportion of the variance in the explanatory variable that can be explained by the response variable(s).

Interpret the slope of the Least Squares Line Equation.

• Income increases by 31.45 with each additional hour worked.

• Income increases by 31.45

• As hours increases by one, income will increase by 31.45, on average

• As hours increases by one, income will increase by 31.45

______________ plot is a scatterplot that displays the residuals on the vertical axis and the explanatory variable on the horizontal axis.

• residual

• predicted

• estimated

• left overs

Shown is a residual plot. Would a linear regression model of the data be most appropriate?

• YES

• NO

Shown is a residual plot. Would a linear regression model of the data be most appropriate?

• YES

• NO

Above is a residual plot from a regression of a variable with the independent variable x. Based on the plot, is it reasonable to conclude that a linear model is appropriate?

• Yes, because the plot shows no apparent pattern.

• Yes, because the points in the plot display less variation as

  x increases.

• Yes, because the sum of the residuals is close to zero.

• No, because the plot shows no apparent pattern.

• No, because the points in the plot display more variation as x

  x increases.

LSRL stands for

• Least Sum Regression Line

• Least Squares Regression Line

• Lower Standard Regression Line

• Line Scatterplot Regression Line

A person travels by car.  They record their miles driven in a data table.  Calculate the linear regression equation of this data.

• y = 61.93x - 1.79

• y = -1.79x + 61.93

• y = 0.016x + 0.03

• y = 0.03x + 0.016

Interpret the slope of the Least Squares Line Equation.

• Income increases by 31.45 with each additional 2 hours worked.

• Income increases by 31.45

• As hours increases by one, income will increase by 31.45.

• As hours increases by one, income will decrease by 242.3.