QUESTION 2 (50 MARKS)

Suppose the Sales manager of the Sweets-4-U2 chain of confectionary stores is interested in the relationship between Sales and Total costs for the Rejoice range of chocolates. i.e. how total cost is affected by sales, for the Rejoice product line.

The 52 Sales and Cost values for both types of chocolate are given in SWEETS-4-U2.xls.

Unless otherwise stated use a level of significance of ? = 0.05.)

(You can use Excel or your calculator for any calculations.)

[a] Obtain the scatter diagram, the covariance and the correlation coefficient for Total Costs and Sales for the Rejoice chocolates. Briefly explain what this graph and these values are telling us about the relationship between Total Costs and Sales

[b] Write down the two forms of the Population Regression function you would assume here. Briefly explain how we interpret the conditional mean E(Y | X) and the error term (?).

[c] Estimate the sample regression function. Write down your estimated model and briefly explain what the estimated intercept and estimated slope are telling us about the relationship between the Total Costs and Sales for Rejoice chocolates.

[d] Using the F statistic, the R-squared value and the p-value for the estimated slope briefly discuss whether this estimated model does or does not show that there is a significant relationship between Total Costs and Sales for Rejoice chocolates.

(With a sample of n = 52 you can assume that the critical values for the t statistic are the same as the critical values for a z statistic.)

Suppose the Sales manager of the Sweets-4-U2 chain of confectionary stores is interested in the relationship between Sales and Total costs for the Rejoice range of chocolates. i.e. how total cost is affected by sales, for the Rejoice product line.

The 52 Sales and Cost values for both types of chocolate are given in SWEETS-4-U2.xls.

Unless otherwise stated use a level of significance of ? = 0.05.)

(You can use Excel or your calculator for any calculations.)

[a] Obtain the scatter diagram, the covariance and the correlation coefficient for Total Costs and Sales for the Rejoice chocolates. Briefly explain what this graph and these values are telling us about the relationship between Total Costs and Sales

[b] Write down the two forms of the Population Regression function you would assume here. Briefly explain how we interpret the conditional mean E(Y | X) and the error term (?).

[c] Estimate the sample regression function. Write down your estimated model and briefly explain what the estimated intercept and estimated slope are telling us about the relationship between the Total Costs and Sales for Rejoice chocolates.

[d] Using the F statistic, the R-squared value and the p-value for the estimated slope briefly discuss whether this estimated model does or does not show that there is a significant relationship between Total Costs and Sales for Rejoice chocolates.

(With a sample of n = 52 you can assume that the critical values for the t statistic are the same as the critical values for a z statistic.)

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