QTM 5 - Correlation and Regression - Tutorial Solutions

# QTM 5 - Correlation and Regression - Tutorial Solutions -...

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1 QTM 5 Correlation and Regression Tutorial Solutions Q1. A shampoo manufacturer is investigating the links between advertising spending and sales. a) Using the data in Excel draw a scatter plot to look for a relationship between advertising and sales. b) Calculate the correlation coefficient for advertising and sales. c) Comment on your results. Solutions a) See Excel b) 0.92 c) There is a strong positive relationship between advertising and sales Q2. A company owns 8 ‘Juice Bars’ in shopping centres such as the Arndale and Trafford centres in Manchester. The company board want to know what effect the shop size has on sales of their various products. a) Using the data in Excel draw a scatter plot to look for a relationship between shop size and sales. b) Calculate the correlation coefficient for shop size and sales. c) Comment on your results from parts a) and b).

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2 Solutions a) b) 0.80 c) The correlation coefficient indicates a strong positive relationship between shop size and sales. However, the scatterplot shows that the relationship between shop size and sales may be non-linear, in other words not a straight line relationship. It looks as though stores over 75m 2 do not produce much more sales. People only want to buy so much juice! Q3 Three graduates of MMU have recently gone into business selling smartphone accessories on Amazon. After several months trading, they’re still unsure as to the effect different price levels for their ‘Speck’ protective cases have on sales. a) Using the data in Excel draw a scatter plot to look for a relationship between price and sales. b) Calculate the correlation coefficient for price and sales. c) Comment on your results from parts a) and b). d) Draw a line chart of sales per month to see if anything else could be ‘driving’ sales of protective cases.
3 Solutions a) b) -0.37 c) The scatterplot seems to show a negative relationship between sales and price as would be expected. However it doesn’t look like a strong linear relationship. This is confirmed by the correlation coefficient which points to a moderate correlation between price and sales. d)

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4 The line chart shows that sales for the business are on a general upward trend, perhaps as they become a more trusted seller on Amazon. There also appears to be a seasonal effect to sales, as sales levels ‘peak’ in December. It looks as though increased ph one sales around Christmas is boosting demand for phone accessories. Q4 JJD Sports are having a tough time. Sales in their 119 stores nationwide have been poor since the start of the recession in 2008.
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