I 4 marks test at the 5 level of significance whether

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(i) [4 marks] Test, at the 5% level of significance, whether the Pearson's correlation coefficient between P/E Ratio and P/B Ratio is greater than 0.7. Instruction: Go to Spreadsheet " Q5(a) " . Perform a nonparametric test for the Spearman's rank correlation coefficient between Yield and Market Capitalisation. (ii) [3 marks] Test, at the 5% level of significance, whether there is a linear relationship between Yield and Market Capitalisation . (b) [8 marks] A junior business analyst of an audit firm is studying the relationship between two accounting variables X and Y. He collects a random sample of 50 pairs of ( X , Y ) values and uses a simple linear regression model to study how variable Y is affected by variable X. The data are saved in Spreadsheet "Q5(b)". Instruction: Go to Spreadsheet " Q5(b) " . Perform a simple linear regression analysis and investigate the residual plot. (i) [3 marks] Write down the model that the business analyst uses. Comment on the residual plot and suggest a better regression model.
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QBUS5001 (2015 Semester 2) – Final Examination - 17 of 17 - (ii) [3 mark] Write down the estimated linear regression equation of the suggested model in (i). Give two reasons why this model is better. Hint: You may need to create an extra variable with values in the spreadsheet. (iii) [2 marks] If the value of X , increases from 20 to 21, find the expected change in the value of Y . (c) [5 marks] A business analyst in the Department of Fair Trade is investigating the collusive bidding amongst the state’s road construction contractors who sometimes set bid prices higher than the fair market price. Suppose an investigator has obtained information on the bid status for a random sample of 31 contracts. In addition, two variables thought to be related to bid status are also recorded for each contract: number of bidders, 1 X , and the difference between the winning (lowest) bid and the estimated competitive bid, 2 X , measured as a percentage of the estimate. The response variable, Y takes value 1 if it is a fixed bid, and value 0 if it is a competitive bid. Let ) 1 ( Y P p and r be the odds ratio of ) 1 ( Y P to ) 0 ( Y P . The data are fitted by a logistic regression model and the estimated regression coefficients are 52 . 1 ˆ 0 , 75 . 0 ˆ 1 and 12 . 0 ˆ 2 . (i) [1 mark] Write down the estimated logistic regression equation that the business analyst can use to predict the probability of a fixed bid. (ii) [1 mark] Interpret the regression coefficient of 2 X . (iii) [3 marks] In a bidding of road construction contract, eight bidders submit a bid and the winning bid is 10% higher than the estimated competitive bid. Estimate the probability that this is a competitive bid. *** END OF EXAMINATION PAPER ***
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