The first model fit to the data was (a) Based on the output for the first model

Question

The first model fit to the data was

(a) Based on the output for the first model a business analyst concluded the following:

Here you provide a detailed critique of the statement. (i) Verify that the predictor variable, Distance is highly significant. What test led to this conclusion and is the analyst correct? (ii) Verify that the model explains 99.4% of the variability of the Y -variable, Fare. Where did this number come from in R summary and how is it derived? Use sum of squares to arrive at the same number. (iii) After checking parts (i) and (ii), make your detailed critique of the conclusion made by analyst.

(b) Does the ordinary straight line regression model (5) seem to fit the data well? If not, carefully describe on how it can be improved.

Given below are some figures and R output:

Explanation / Answer

From the plot of fare versus distance we observe that the points are close to the regression line and so high variability in fare is explained by distance.

From scatter plot of standardized residuals versus predictor distance we observe that there are two points which have residuals >=2 in magnitude and both are for high values of distance and so are potential influential observations. Hence, regression model does not seem to be valid as also we observe from this plot a curve in points

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