220MP: Linear Statistical Models - Open Time Constrained - Engineering Assignment Help

Assignment Task:

(a) Give the one-way analysis of variance model relevant to the analysis of this data. Define any notation clearly.
(b)Construct the one-way analysis of variance table.
(c)Carry out the relevant F test giving full details and your conclusion.
(d)Compare the residuals for each area (or the sales) over the four months period. What do you conclude? What further analysis would you suggest?
(e)Give a 95% confidence interval for the mean sales in Area 1 and interpret.

2. Three different pesticides (labelled 1, 2 and 3) were tested on a potato crop at two different times during the season, i.e. ‘Early’ and ‘Late’. The field was divided into 30 equal-sized plots and each combination of pesticide and timing was tried on five different plots.

At the end of the growing season the yield of potatoes (kg) from each plot was recorded. The table below shows the mean yield per plot for each combination of pesticide and timing:

(c) Test the significance of the interaction term and interpret in context.
(d) Carry out a Bonferroni least significant difference analysis to determine which combination of pesticide and timing gives the highest yield on average. Use a 3% family significance level. Explain your method and state your conclusions clearly.

4. Data were collected on the average cost (£) of return economy tickets for flights on 11 routes for each of two airlines A and B. The distances (miles) for these routes were also recorded. Variable Airline was defined as: Airline = 0 for A, and = 1 for B.

The data were analysed using Minitab. Parts of the output are given below. Use these to answer the following questions.

5. For this question we use the same scenario as in question 4 above. The scenario is repeated below.

Data were collected on the average cost (£) of return economy tickets for flights on 11 routes for each of the two airlines A and B. The distances (miles) for these routes were also recorded. Variable Airline was defined as: Airline = 0 for A, and = 1 for B.

The data were analysed using Minitab. Parts of the output are given below. Use these to answer the following questions.

(a)i. Give the theoretical form of the model fitted below and interpret its meaning in context.
ii. Give the fitted equations for the two airlines and discuss their differences in context.
iii. Use an F test to test for inclusion of the Distance × Airline term, giving full details and interpret your result.
iv. Calculate the leverage for observation 20 and comment on its value.

(b) Research has shown that many other variables could affect the cost of air travel such as the duration of flight, timing of the purchase, timing of flights (e.g. peak or off peak), day of flight (e.g. week day or weekend), airport size, season of travel, airport distance from a main city, major or regional airport, budget or major airline.

Having considered this briefly describe how you would go about improving the above model from part (a).

(c) What problem could arise when both duration of the flight (i.e. the time taken) and distance are included in a model? Discuss.

Explain how heteroskedasticity could arise when only distance is included in the model.

6. The seasonally adjusted quarterly data for the number of fatal injuries due to road accidents were recorded for the last 39 quarters. Below is a plot of the data against time in quarters. The data were analysed using Minitab. Parts of the output are given below. Use these to answer the following questions.

(a)i. Use the plot above to describe the pattern of the trend over time. Discuss the validity of the model below fitted to the data.
ii. Interpret the 95% CI given in the output below.
iii. Describe the relevance of the Durbin Watson test statistic and use the relevant result in the output below to carry out this test giving full details.

Appendix 1: Statistical Tables

t-Distribution Tables

F- Distribution Tables

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