Statistics Linear Regression: Suppose researchers fit the simple linear regressi

Question

Statistics Linear Regression: Suppose researchers fit the simple linear regression model in order to study the relationship between a predictor variable, X, and a response variable, Y. Based on the diagnostic plots produced in SAS, comment on the validity of the fallowing assumptions: linearity, constant variance, and normality. Justify your answers, a simple yes or no answer is not sufficient. Fit Diagnostics for y 10.0 7.5 C5.0 2.5 0.0 2.5 8o 0 8 4 6 8 10 12 14 Predicted Value 4 6 8 10 1214 Predicted Value 0.01 0.02 0.03 0.04 0.05 Leverage 20 0.08 0.06 0.04 0.02 0.00 15 10 -2 1 0 2 Quantile 10 15 20 100 Predicted Value Observation Fit-Mean Residual 40 30 Observations 128 Parameters Error DF MSE R-Square Adj R-Square 0.5011 D 20 126 4.4704 0.505 6 3 0 3 6 9 0.0 0.4 0.8 0.0 0.4 0.8 Residual Proportion Less

Explanation / Answer

In the given plots, the first and second plot show a constants variance because the data is not more vare. The maximum data is the range 6 to 12 . when we divided in some interval then the variance is constant.

in the third plot there is some outliers which effect the model but the is look like normal.

The 4th plot show the quantile plot which is a q-q plot of normal distribution

the 5th plot is a linear function because all points are cover in the linear line.

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