Why is regression analysis used?
- Predict the value of a dependent variable based on the value of at least one independent variable
- Explain the impact of changes in an independent variable on a dependent variable
What are the 4 assumptions of linear regression model
- Linearity
- independence of errors
- Normality of error
- Equal variance
what is linearity?
States that the relationship between variables is linear (Straight line)
What is independence of errors?
requires that the errors are independent of each other. Assumption is important when data is collected over a period of time
What is Normality of error?
requires that the errors are normally distributed at each value of X
what is constant/equal variance?
or homoscedasticity, requires that the variance of the errors be constant for all values of X. In other words, the variability of Y values is the same when X is a low value as when X is a high value
Multiple R
- It is the absolute value of correlation coefficient between y & x
Example: Multiple R of 0.98546 means that X and Y have a high positive correlation
R squared
- Measure the % of variation in the dependent variable that can be explained by the linear relationship between x & y
- Example: R square of 0.58082 means 58.08% of the variation in Y is explained by the variation in X
Adjusted R squared
– used in place of R Squared if there are multiple x’s (independent variables)
Standard error
- a measure of the variation of observed y vales from the regression line. (the smaller the value the better)
Observations
- sample size
ANOVA
- tests the overall significance of the regression. If the p-value (significance F) is <0.05 the relationship is meaningful and there is a linear relationship between x & y
