Linear Regression

Question 1

What is correlation used for?

Answer 1

measuring the strength and direction of a linear relationship

Question 2

What is regression used for?

Answer 2

describing the linear relationship with an equation for other groups or for other situations

Question 3

When do you use regression?

Answer 3

when only data on the independent variable is known

Question 4

what variable is being predicted in single linear regression?

Answer 4

the dependent variable, y

Question 5

what variable is used to make predictions from in single linear regression?

Answer 5

the independent variable or the predictor, X

Question 6

How do you determine the equation of the best fitting line?

Answer 6

a technique called least squares regression

Question 7

what are residuals?

Answer 7

the difference between the observed value of y and the predicted value of y (point on the line)

Question 8

what do the residuals look like when the line fits the data well?

Answer 8

they are small

Question 9

what regression equation is the best?

Answer 9

the one with the smallest sum of squared residuals

Question 10

how do you measure the accuracy of the predictions?

Answer 10

standard error of the estimate AKA root mean squared error (RMSE)

Question 11

what is the RMSE?

Answer 11

root mean squared error, the average error we make when using the regression equation to make predictions

Question 12

what is the regression equation?

Answer 12

y = b0 + b1x where b0 is the y-intercept and b1 is the slope

Question 13

what is the coefficient of determination?

Answer 13

R^2 = the percentage variance or measure of how well the line represents the data?

Question 14

what can you do to test if the linear relationship is a significant relationship?

Answer 14

test for the slope (t-test) and test for explained variance (f-test)

Question 15

what does the t-test test?

Answer 15

test for the slope = if the slope differs from 0

Question 16

what are the hypotheses for the t-test?

Answer 16

H0: B1 = 0
HA: B1 ≠ 0

Question 17

What does the f-test (test for explained variance) test for?

Answer 17

if the proportion of the variation that is explained by the model is significantly greater than 0

Question 18

What are the hypotheses for the f-test?

Answer 18

H0: p^2 = 0
HA: p^2 > 0

Question 19

what are the unstandardized regression coefficients?

Answer 19

b0 and b1, these are expressed in the same units as the dependent variable

Question 20

what is the standardized regression coefficient?

Answer 20

coefficient beta, it is equal to the correlation coefficient r

Question 21

What does the coefficient beta measure?

Answer 21

the change in Y in SD’s when X increases by 1 SD

Question 22

when is the coefficient beta useful?

Answer 22

1. when the units of measurement of X and Y differ dramatically
2. when we use more than 1 independent variable to predict Y and we wish to compare the importance of them

Question 23

What does multiple linear regression allow for?

Answer 23

adding multiple independent variables to predict the dependent variable

Question 24

what is the equation for MLR?

Answer 24

y = b0 + b1x1 + b2x2 … + bkxk

Question 25

what does adding more independent variables to a model (MLR) do?

Answer 25

1. explain more of the variation of the dependent variable (R^2 will increase)
2. reduce the average prediction error (the SE decreases > accuracy of prediction increases

Question 26

how can you find the significance of individual predictors?

Answer 26

using the t-test

Question 27

which predictor in MLR has the most impact on changes in the Y-variable?

Answer 27

the one with the largest standardized coefficient

Question 28

what are the assumptions for linear regression?

Answer 28

1. normality (use histogram)
2. homoscedasticity
3. linearity
4. no outliers (between -3 and 3)