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ECON7300: Statistical Project Assignment (Part II), Semester 1, 2023

Instructions for Dataset2_part2: Simple Regression Analysis

A sample size of 170 is taken from bus users in country S to investigate the relationship between travel cost (tcost) and travel time (ttime). The variables in the dataset are:

•   tcost (Y, in dollars)

•   ttime (X, in hours)

The dependent variable for your analysis is tcost.

Answer the following questions using Dataset2_part2.

(a) Estimate a regression model using X to predict Y (state the simple linear regression equation).

(b) Interpret the meaning of the slope.

(c) Predict Y when X = 0.85

(d) Compute the coefficient of determination and interpret its meaning.

(e) Compute the standard error of the estimate and interpret its meaning. Judge the magnitude of the standard error of the estimate.

(f)  Perform a residual analysis (plot the residuals) and evaluate whether the assumptions of regression have been violated.

(g) Test for the slope using t test (follow all the necessary steps). Assume 5% level of significance.

(h) Test for the slope using F test (follow all the necessary steps). Assume 5% level of significance.

(i)  Test for the correlation coefficient (follow all the necessary steps). Assume 5% level of significance.

(j)  Compute a 95% confidence interval estimate of the mean Y for all bus users in country S when X = 0.85 and interpret its meaning.

(k) Compute a 95% prediction interval of Y for a bus user in country S when X = 0.85 and interpret its meaning.