(12 marks for a & 4 marks for f the \"On the first crime rates undertaken, in En
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(12 marks for a & 4 marks for f the "On the first crime rates undertaken, in England, by John in 1857, and titled Religiou worship, Attendance on 40 English Relation Between of the and Beer Aggregate data was collected The variables are: Criminal per 100k population Ale/Beer Houses (Pubs) per 100k population Attendants at school per 10k population Attendants at public worship per 20oo population Using R, we examine three simple Linear Regression models. 500 700 900 1100 600 800 1000 1200 100 300 500 700 school pubs Res QQplot Model 3 Res QQplot Model 1 Res QQplot Model 2 Theoretical Quanties Theoretical Quant Theoretical QuantiesExplanation / Answer
a) The qq plot seems fine for all the 3 models. There is not much deviation observed. Heavier tails and lighter tails are not that much prominent in the images shown, indicating that residuals are approximately normally distributed. Its better to check the residuals vs fitted values plot to see if some pattern is present.
b) Model 1 seems to be the best model among the three models given i.e. based on pubs variable. Residual standard error is minimum for this model compared to other two. R squared value is .2142, that means 21.42% of variance in the number of criminals can be attributed to pubs variable.
c) Model 1 has the best predictor. As the p value associated with it is less than 0.05, that means it is statistically significant. Here Null hypothesis is that slope is 0. Alternative hypothesis is slope is not zero. t statistic value is 3.219. The distribution is t distribution. p value is 0.00263. Conclusion is we reject the null hypothesis i.e. slope is not zero.
d) The best model is Model 1. Based on this model, our regression line is:
y = 109.34 + 0.1162 * x
y = 109.34 + 0.1162 * 300 = 144.2
So around 144 criminals.
e) Interpretataion is - For every one unit increase in no. of pubs per 100 k population, the no. of criminals per 100k of population is getting increased by 0.1162
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