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1. Use appropriate graphs to interpret the relationship between (i) psychological health and commuting time; (ii) psychological health and wage; and (iii) psychological health and age. Carefully interpret and explain.

2. Calculate the sample correlation and covariance for the above 3 relationships in question 1 using Data Analysis Tool Pack. In addition, for the relationship between psychological health and commuting time, you are required to calculate the sample correlation and covariance using a second method (using basic Excel formulae without Data Analysis Tool Pack). The calculations by the second method should be carefully laid out in Excel and should NOT use any hard-wired Excel statistical functions e.g. COVARIANCE.S, CORREL, et al. You can use the Excel sort command, the sum command, and any other non-statistical excel commands). Carefully interpret your results.

3. Use simple regression to explore the relationship between (i) psychological health (Y) and commuting time (X); (ii) psychological health (Y) and wage (X), respectively. You may use Data Analysis Tool Pack for this. Based on the excel regression output, first write down the estimated regression equations, then carry out any relevant two-tailed hypothesis tests using the critical value approach at the 5% significance level. Carefully interpret your hypothesis test results.

4. Now use multiple regression to explore the relationship of psychological health (Y) with, commuting time (X1), age (X2) and wage (X3). You may use Data Analysis Tool Pack for this. Based on the excel regression output, first write down the estimated regression equation, then carry out any relevant two-tailed hypothesis tests using the critical value approach at the 5% significance level, and an overall significance test using the p-value approach. Carefully interpret your hypothesis test results

5. Using your multiple regression results to predict psychological health for a typical worker with commuting time equal to: (i) 0.5 hour; (ii) 2.0 hour, respectively. Here we assume that age (X2) and wage (X3) take their sample mean values. (Hint: this means you will have 2 distinct predictions for psychological health.) Carefully interpret your results.

6. Workers’ psychological health may be impacted by other factors too. If you could request additional data to study the determinants of workers’ psychological health, what extra variables would you request? Illustrate two such variables. Carefully explain why you choose these two variables (by drawing evidence from the literature such as journal articles, newspapers, et al), types of your proposed variables (e.g. numerical or categorical), and how each of your proposed variables will be measured in the regression model.

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