Results

Linear Regression

Overall, the model is a significant fit to the data, F(3, 227) = 17.07, p < .001 (see ANOVA). The adjusted 𝑅²(0.173) suggests that 17.3% of the variance in salaries can be explained by the model when adjusting for the number of predictors.

Model Summary - salary
Model	R	R²	Adjusted R²	RMSE
M₀	0.000	0.000	0.000	16.026
M₁	0.429	0.184	0.173	14.572

Note. M₁ includes age, years, status

ANOVA
Model		Sum of Squares	df	Mean Square	F	p
M₁	Regression	10871.964	3	3623.988	17.066	< .001
	Residual	48202.790	227	212.347
	Total	59074.754	230

Note. M₁ includes age, years, status
Note. The intercept model is omitted, as no meaningful information can be shown.

Coefficients
							Collinearity Statistics
Model		Unstandardized	Standard Error	Standardized	t	p	Tolerance	VIF
M₀	(Intercept)	11.338	1.054		10.753	< .001
M₁	(Intercept)	-60.890	16.497		-3.691	< .001
	age	6.234	1.411	0.942	4.418	< .001	0.079	12.653
	years	-5.561	2.122	-0.548	-2.621	0.009	0.082	12.157
	status	-0.196	0.152	-0.083	-1.289	0.199	0.867	1.153

Based on the Coefficients table, it seems as though salaries are significantly predicted by the age of the model. This is a positive relationship (look at the sign of the beta), indicating that as age increases, salaries increase too. The number of years spent as a model also seems to significantly predict salaries, but this is a negative relationship indicating that the more years you’ve spent as a model, the lower your salary. This finding seems very counter-intuitive, but we’ll come back to it later. Finally, the status of the model doesn’t seem to predict salaries significantly.

The next part of the question asks whether this model is valid (we will examine the assumptions).

1. Multicollinearity: For the age and years variables, VIF values are above 10 (or alternatively, tolerance values are all well below 0.2), indicating multicollinearity in the data (see above). This indicates these variables may measure very similar things. Of course, this makes perfect sense because the older a model is, the more years she would’ve spent modelling! So, it was fairly stupid to measure both of these things! This also explains the weird result that the number of years spent modelling negatively predicted salary (i.e. more experience = less salary!): in fact if you do a simple regression with years as the only predictor of salary you’ll find it has the expected positive relationship. This hopefully demonstrates why multicollinearity can bias the regression model.

Collinearity Diagnostics
				Variance Proportions
Model	Dimension	Eigenvalue	Condition Index	(Intercept)	age	years	status
M₁	1	3.925	1.000	0.000	0.000	0.001	0.000
	2	0.070	7.479	0.009	0.000	0.080	0.016
	3	0.004	30.758	0.299	0.017	0.013	0.944
	4	9.781×10^-4	63.344	0.692	0.983	0.906	0.040

Note. The intercept model is omitted, as no meaningful information can be shown.

Influential Cases
Case Number	Std. Residual	salary	Predicted Value	Residual	Cook's Distance
5	4.697	95.338	28.265	67.073	0.227
116	3.440	64.791	14.926	49.865	0.031
135	4.717	89.980	21.895	68.085	0.108
155	3.319	74.861	27.403	47.458	0.106
191	3.178	50.656	4.716	45.939	0.041
198	3.531	71.321	20.173	51.148	0.038

2. Residuals: In Influential Cases there are six cases that have a standardized residual greater than 3, and two of these are fairly substantial (case 5 and 135). We have 5.19% of cases with standardized residuals above 2, so that’s as we expect, but 3% of cases with residuals above 2.5 (we’d expect only 1%), which indicates possible outliers.E

3.Homoscedasticity: The scatterplot below of Residuals vs Predicted does not show a random pattern, with visible funneling, indicating heteroscedasticity thereby violating the assumption of homoscedasticity.

Residuals vs. Predicted

Q-Q Plot Standardized Residuals

4.Normality of errors: In the normal Q–Q plot above, the dashed line deviates considerably from the straight line (which indicates what you’d get from normally distributed errors). This indicates the normality of errors assumption has been broken.

Conclusion about model fit:

Due to the multicollinearity, large residuals for certain cases, and violation of homoscedasticity, it can be concluded that several assumptions have not been met and so this model is probably fairly unreliable.