Chapter 10 - Simple Linear Regression Flashcards
State the simple linear regression model
State the formula for residuals in Simple Linear Regression
State the formula for sum squares of Y
State the formula for the sum squares of X
State the formula for the sum of squares X & Y
State the formula’s to determine the Simple Linear Regresion line
What is the sum squares of the residuals?
All the variation not explained by the model
What is the sum square of reggresion?
What is the total of sum of squarse? In simple linear regression
What is SS-total equal to when there is no correlation in simple linear regresion analysis?
How is an ANOVA table laid out for linear regression?
State the distrubution of b1 in simple linear regression
s = sqr(SS-res/(n-2))
What is the correlation coefficient?
What is the r^2 ?
Square of the correlation coefficient, also equal to (SS-reg/SS-total)
What are the assumptions of simple linear regression?
- Linear model is appropriate
- Error terms are normally distributed
- error terms have constant variance
- error terms are uncorrelated
When r^2 = 0, what is SS-total equal to?
r = 0, b1 = 0, SS-reg = 0, SS-total = SS-res
In simple linear regression, when are points considered outliers?
When they have a normal residual > 2 in magnitude
In simple linear regression, how can we check that the linear model is appropriate?
1) scatterplot of xi & yi should show points rougly around a line
2) scatter plot of standardised residuals against fitted values should not have a pattern
3) scatter plot of standardised residuals against xi should not have a pattern
In simple linear regression, how can we check that errors are normally distributed?
a) Histogram of residuals should look normal
b) Normal probability plot should have a straight line
If the data is right skewed, fix by sqr(), cubert() or log() to the y value (in increasing severity)
If the data is left skewed, fix by sqr(), cube(), exp() to the y value (in increasing severity)
In simple linear regression, how can we check that errors have constant variance?
A scatterplot of standardised residuals against xi and fitted values should show constant spread.
In simple linear regression do we check if the errors are correlated?
Not in this course we don’t
