Linear Regression Questions with Correct
Answers 2025
Simple Linear Regression - correct answers-Describes the relationship between the values of two
continuous variables where there is only one explanatory/independent variable; however, if model is
not available then the mean of Y is the best estimate.
Assumption for Simple Linear Model - correct answers-Y = alpha + beta(X) + error term where the error
term is roughly equivalent to the population distribution of N(0, variance)
Y definition - correct answers-Response/ Dependent Variable
alpha definition - correct answers-The Y intercept/ Expected value of Y when X = 0
beta definition - correct answers-Regression coefficient/ slope of the line/ Amount of change in Y for a 1
unit change in X; when the slope = 0 there is a horizontal line and it indicates no relationship
X definition - correct answers-Predictor/ Independent Variable/explanatory variable
epsilon definition - correct answers-Error term (since not all points will lie on the line exactly) Error
explains other factors that are influencing the data
Least Squares Regression - correct answers-The method that minimizes the sum of the squares of the
vertical distances of the observations from the line; We find the difference between the observed value
and the expected (predicted) value (otherwise known as the error or residual). Each error is squared
because we are not interested in whether + or -. The method chooses the intercept and slope in a way
that makes the sum of the residuals squared as small as possible
Fitted Line equation - correct answers-Y(hat) = a + bX
Y hat is the predicted value.
Residuals equation - correct answers-e = Y - Y(hat); the observed - the predicted value
Estimating alpha, beta, and the population variance - correct answers-1) b = (X- Xmean)(Y-Ymean) / (X-
Xmean)^2 (slope)
2) a = Ymean - bXmean (intercept)
OR
SSxx (Sum of X)^2 / n
SSyy (Sum of Y)^2 / n
SSXY (Sum of X)(Sum of Y) / n
Answers 2025
Simple Linear Regression - correct answers-Describes the relationship between the values of two
continuous variables where there is only one explanatory/independent variable; however, if model is
not available then the mean of Y is the best estimate.
Assumption for Simple Linear Model - correct answers-Y = alpha + beta(X) + error term where the error
term is roughly equivalent to the population distribution of N(0, variance)
Y definition - correct answers-Response/ Dependent Variable
alpha definition - correct answers-The Y intercept/ Expected value of Y when X = 0
beta definition - correct answers-Regression coefficient/ slope of the line/ Amount of change in Y for a 1
unit change in X; when the slope = 0 there is a horizontal line and it indicates no relationship
X definition - correct answers-Predictor/ Independent Variable/explanatory variable
epsilon definition - correct answers-Error term (since not all points will lie on the line exactly) Error
explains other factors that are influencing the data
Least Squares Regression - correct answers-The method that minimizes the sum of the squares of the
vertical distances of the observations from the line; We find the difference between the observed value
and the expected (predicted) value (otherwise known as the error or residual). Each error is squared
because we are not interested in whether + or -. The method chooses the intercept and slope in a way
that makes the sum of the residuals squared as small as possible
Fitted Line equation - correct answers-Y(hat) = a + bX
Y hat is the predicted value.
Residuals equation - correct answers-e = Y - Y(hat); the observed - the predicted value
Estimating alpha, beta, and the population variance - correct answers-1) b = (X- Xmean)(Y-Ymean) / (X-
Xmean)^2 (slope)
2) a = Ymean - bXmean (intercept)
OR
SSxx (Sum of X)^2 / n
SSyy (Sum of Y)^2 / n
SSXY (Sum of X)(Sum of Y) / n
