Question

i do not know how to interpret these graphs. please when exlaining do not write the definition and instead can you write whats going on in the graphs like the errors. alos air pop in the graph means air pollution

Residuals vs Fitted 0151 3 OO Oo 1850 450 60 65 70 75 80 Fitted values Im(Malelife GDP + ruralpop + airpop) Normal Q-Q 1510 045 0185 2 -3 2 -1 1 3 Theoretical Quantiles Im(Malelife- GDP+ ruralpo+ airpop) Scale-Location 1850 450 0151 o Oo 。。。。。。。。 ooooo。 80 75 70 65 60 Fitted values Im(Malelife GDP+ ruralpop + airpop) Residuals vs Leverage 0151 0.5 o175 0.5 Cook's distance 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Leverage Im(Malelife GDP+ ruralpop+ airpop)

Answer 1

Here from the first plot, Residual versus fitted values plot there is some pattern in the data. The points are are not scattered. the residuals appear on the y axis and the fitted values appear on the x axis. From the plots, which seem to indicate dependency between the residuals and the fitted values, suggest a different model. Therefore the problem of heteroscedasticity exist. From the QQ plot it is clear that the residuals are not normal. The model does not satisfy the model assumptions. Therefore the model is not adequate.

the third plot also called Spread-Location plot. This plot shows if residuals are spread equally along the ranges of predictors. It’s good if you see a horizontal line with equally (randomly) spread points.the residuals are spread around 70 then it become narrower along the x-axis as it passes around 80.

The last plot helps us to find influential cases if any. Not all outliers are influential in linear regression analysis. Even though data have extreme values, they might not be influential to determine a regression line. That means, the results wouldn’t be much different if we either include or exclude them from analysis. On the other hand, some cases could be very influential even if they look to be within a reasonable range of the values. They could be extreme cases against a regression line and can alter the results if we exclude them from analysis. Another way to put it is that they don’t get along with the trend in the majority of the cases. When cases are outside of the Cook’s distance (meaning they have high Cook’s distance scores), the cases are influential to the regression results. The regression results will be altered if we exclude those cases. in last plot, a case is far beyond the Cook’s distance lines (the other residuals appear clustered on the left).The plot identified the influential observation as 231. If we remove the value from the regression then the the coefficients and R² value all will change......