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Simple linear regression
Has only one x and one y variable
Whats the difference btw multiple and
Differnece of number of variables we are including
Multiple linear regression
Has one y and two or more x variables
Example of simple linear regression
We predict rent based on square feet alone
Example of multiple linear regression
Predict rent based on square feet and age of the building
if more than one independent variable is to be used in the regression model, linear regression can be extended to
Multiple regression to accommodate to several independent variables for prediction
What happens when we add more variables
adding more predictive power to model
R and R2 will either stay the same or improve
Residuals are generally closer to 0
Adding more independent variables to a model tends to
Improve prediction
Residuals are closer to 0 because we minimuze
epsilon, random error.
Categorical variable
Type
Impact of carat weight on diamond price (regression results)
We expect price goes up by 5333.86 on average
Multiple regression analysis additional statement (IMPROTANT)
controlling for the effect of other variables ; keeping other variables constant ; ceteris paribus ( ALL THIS MEANS Incremental impact on that specific variable)
Estimation power of ANOVA test (on sldies)
Reject null hypothesis and conclude that at least one of the models variables is significant (significance is less than .05) (on the price of diamonds)
Is it approproiate to interpret? (analyzing each coefficient)
if p vall is greater than .5 and 0 is in the range
Adjust R square is a modified version of R-Squared that
has been adjusted for the number of predictors in the model
For multiple regression analysis we use
ADjusted R2
R2 indicates how well
actual data points fit a line but adjusts for the number of terms in a model
The adjusted R-Squared value increases only when the new term
improves the model fit more than would be expected by chance
The adjusted R-Squared value decreases when a
Predictor improves the model by less than expected
R squared value always increases when
The number of variables increases
R -Squared values will still increase if you add a useless
variable to the model
Adjusted R-Squared value will
never increase if you add a useless X-Variable to the model
Adjusted R-Squared is mainly used for
the model selectiom but not the R-Squared value is used
Multicollineraity is a statistical phenomenon that occurs when
Two or more predictor variables in a regression model are highly correlated
Consequences of Multicollinearity
makes it challenging to determine the individual effect of each variable on the dependent variable
Multicollinearity may appear that some variables are
not significant when they might be individually, and vice versa
If multicollinearity is present in a regression model, it does not necessarily invalidate the model but it can
affect the precision of coefficient estimates. May lead to unstable and unpredictable coefficient values