MLR

Question 1

How is the best regression model fit found?

Answer 1

The best fit model is the one that minimises the total square differences between the X data points and the model.

Question 2

What is simple linear regression?

Answer 2

A statistical technique that develops an equation that relates a dependent variable to one independent variable.

Question 3

What does SLR do?

Answer 3

1) Enables prediction of dependent variable
2) Estimates the line of best fit
3) Evaluates a linear relationship between the explanatory variable and the response variable.

Question 4

An important tip for interpreting SLR model?

Answer 4

The coefficient of X shows an increase/ decrease ON AVERAGE not certainly. The Y-intercept shows the AVERAGE is not accurate.

Question 5

What is the lower and upper 95%?

Answer 5

This is the 95% confidence interval around the estimated values. Shows the amount of variability in the models.

Question 6

How to find the T-value in Excel?

Answer 6

T.INV.2T(CI/2, number of values - number of variables -1)

Question 7

What does the estimated slope do?

Answer 7

Provide information about the relationship between the response variable and the explanatory variable. It also shows the estimated average increase in Y for a one-unit increase in X.

Question 8

What does the intercept show?

Answer 8

The value of the predicted response when the explanatory variable value is zero.

Question 9

What does the t-test in the SLR model show?

Answer 9

These show whether the coefficient values are significantly different from 0. E.g. if floor space significantly explains the variability in house prices.

Question 10

How to carry out a t-test?

Answer 10

Step 1: H0: beta=0 H1: beta =/ 0
Step 2: Assume H0 is true.
Step 3: Calculate the test statistic
t= (coefficient estimate-0)/ SE(coefficient estimate)
Step 4: Interpret results.

Question 11

What does the p-value show?

Answer 11

The p-value shows the sum of the two cut-off areas of the distribution in a two-tailed test. It shows the probability of getting the t-stat or more extreme given the null hypothesis is true.

Question 11

What is the connection between the confidence interval and 2 tailed t-tests?

Answer 11

If the t-test shows that the coefficient is significantly different from 0 p<aplha then the confidence interval doesn’t contain 0. If the opposite occurs the CI does contain 0/

Question 11

What does the t-test test for?

Answer 11

Whether the coefficients are significantly different from 0.

Question 12

What does the SS of regression show?

Answer 12

This shows the sum of the squares of the differences between the predicted values and the mean of the data points. Shows the total variation of the response variable.

Question 13

How to find SS Total?

Answer 13

SS regression + SS residual

Question 14

How to find the R-squared value?

Answer 14

SS regression/ SS total.

Question 15

What does R squared show?

Answer 15

It shows how much of the variation is explained by the model. It evaluates the dispersion of the data points around the fitted regression line. Also called the coefficient of determination.

Question 16

Why is the R-squared value not always good?

Answer 16

1) Doesn’t show outliers.
2) Doesn’t show increasing variance.
3) Doesn’t show model is curved.

Question 17

What is heteroscedasticity?

Answer 17

The variance differs over the data set.

Question 18

When can you carry out a SLR model?

Answer 18

1) When the residuals have constant variance.
2) The model must be linear.
3) Residuals must be uncorrelated.
4) The errors are normally distributed with a mean of 0.

Question 19

What does the standard error show?

Answer 19

This is the average distance that the observed data points fall from the regression line. I.e. it tells you how wrong the model is on average using the units of the response variable.

Question 20

How to calculate the standard error?

Answer 20

Mean squared residual value square rooted.

Question 21

How to calculate multiple R?

Answer 21

The square root of the R squared value.

Question 22

What is the multiple R?

Answer 22

This is the correlation coefficient. Shows how strong the linear relationship is between the response y data and explanatory x data.

Question 23

What does F show?

Answer 23

1)
It tests whether the model ‘taken as a whole’ is explaining a significant portion of the variability in the response variable
2)
It tests the null hypothesis that a model with no explanatory variables fits the data as well as your fitted regression model.

Question 24

What is step 1 of the f-test?

Answer 24

H0: a model with no explanatory variables fits the data as well as this model.
H1: your model fits the data better than the intercept-only model.

Question 25

How to find the f-test statistic value?

Answer 25

MS regression/ MS residual

Question 26

How to calculate the residuals?

Answer 26

Observed value for response - predicted value from the model.

Question 27

How to check that the regression assumptions hold?

Answer 27

Using the residuals

Question 28

What is a MLR model?

Answer 28

It includes more than one explanatory variable with the same assumptions as the SLR model.

Question 29

How do we account for models with more than two categories in the explanatory variable?

Answer 29

By using dummy variables (binary variables). Always use one less than the number of categories.

Question 30

What is the reference category?

Answer 30

All the dummy variables are equal to 0. When interpreting the fitted model, comparisons are made with respect to the reference category.

Question 31

Interpreting dummy variables

Answer 31

If significant variability in the response variable is explained by at least one of the dummy variables we must keep the rest even if they don’t.

Question 32

What is a binary variable?

Answer 32

A variable that can only take two values.

Question 33

How would you interpret D1 from the following equation?
Sale Price = 17640.7 + 107.5 Floor Space - 46898.1 D1 -58001.8 D2

Answer 33

The sale price decreases on average by $46898 if it’s a two-family conversion compared with the reference category assuming floor space stays set.

Question 34

What is multicollinearity?

Answer 34

Where one explanatory variable in an MLR model can be predicted from one or more other explanatory variables in the model. E.g. aX1+bX2+cX3= X4

Question 35

Which of the following is a possible effect of having multicollinearity in your model?

Answer 35

Impacts calculations regarding individual explanatory variables. This in turn means cannot rely on the interpretation of the coefficient values as an explanation for relationships between Y and X.
It can also affect the validity of p-values.

Question 36

When does multicollinearity occur?

Answer 36

Occurs when two or more explanatory variables in a regression model are moderately or highly correlated with each other.

Question 37

Ways to spot multicollinearity

Answer 37

1) Think about definitions of the variables and whether they overlap.
2) Draw scatter plots and calculate correlations between each pair of explanatory variables.
3) Check whether the fitted coefficient values make sense.
4) Check for a contradiction between the overall ANOVA f-test and individual coefficient t-tests.
5) Play around with the model and see if the coefficients change drastically.
6) Removal of a variable from the model leads to an increased R-squared.

Question 38

How to fix multicollinearity?

Answer 38

1)Try not to include highly correlated explanatory variables.
2) Create a new variable which is a combination of the highly correlated variables.