Understanding Simple Linear Regression: R-squared, Slope, and Conditions
Classified in Mathematics
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Write an interpretation of r^2 using the template in the Activity 2.1 Readings. We will do this one as a class.
Template: The proportion of the variation in the Y variable that is explained by the SLR model with the X variable is r^2.
For slope : Template: As x var increases by 1 unit, we predict y var will increase/dec by ____ y var units.
For y-intercept: When x var = 0 units, we predict that the y var will be ____ units..
For SLR: Error = epsilon = y - yhat = y - (betahat0 + betahat1x)
SSE = residual1^2 + res. 2^2 +…+ res. n^2
Standard error of regression = Root MSE (in SAS language)
The text lists six conditions for simple linear regression. They are:
Condition 1. Linearity – The relationship between X and Y follows a straight line.
Condition 2. Zero Mean – The mean of the errors is 0.
Condition 3. Uniform Spread – The variability in the errors does not change as X changes.
Condition 4. Independence – The value of the error for one observation is not related to the value of the error for any other observation.
Condition 5. Normality – The errors follow a normal distribution.
Condition 6. Randomness – The errors come from data collection done by random sampling or random assignment of individuals to treatments.
Write an interpretation of r^2 using the template in the Activity 2.1 Readings. We will do this one as a class.
Template: The proportion of the variation in the Y variable that is explained by the SLR model with the X variable is r^2.
For slope : Template: As x var increases by 1 unit, we predict y var will increase/dec by ____ y var units.
For y-intercept: When x var = 0 units, we predict that the y var will be ____ units..
We are confidence level % confident that for population the mean Y variable when X variable = value of X will be between lower limit of C.I. unit of Y variable to upper limit of C.I. unit of Y variable
We predict that for confidence level % of population when X variable = value of X the Y variable will be between lower limit of P.I. unit of Y variable to upper limit of P.I. unit of Y variable.
Template: For population we have / do not have a statistically significant linear relationship between Y variable and X variable.