The Question.

Fullparts PLC sells products across the UK which they divide up into 23 sales territories which are coded A-W. You have been asked to perform a regression analysis to predict the sales () of a particular product in each territory from the market potential (estimated total industry sales () for the sales territory). The plot below displays the data which was collected from the previous financial year.

Data and transfer check

Download the data and transfer it into SPSS.

Check that your data transfer has been successful by obtaining the Std. Error of the means for the numeric variables in your data which should appear in SPSS output as:

Sales 429.756

Potential 3181.853

If you do not have these exact values, then you may have not transferred your data from the Excel file to SPSS correctly. Do not continue with the test until your value agrees as otherwise you may not have correct answers.

Unless otherwise directed you should report all numeric values to the accuracy displayed in the SPSS output that is supplied when your data has been transferred correctly.

1. Correlation analysis

Calculate the Pearson's correlation coefficient between Sales and Potential.

Complete the following using Evans (1996) to quantify the strength of correlation:

r= which is a Select very weak weak moderate strong very strong Select positive negative correlation.

Complete the following summary concerning the formal testing of the correlation.

H₀: There Select is is no correlation between Sales and Potential H₁: There Select is is no correlation between Sales and Potential

Asp= we Select reject do not reject the null hypothesis and conclude that there Select is is not a significant correlation between Sales and Potential.

2. Fitted regression model

Use SPSS to perform simple linear regression of Sales on Potential.

What is the regression equation?

Select Sales Potential = + Select Sales Potential

What percentage of the variation is explained by the model? (1 d.p.)

What percentage of the variation is not explained by the model? (1 d.p.)

How many outliers (|standardised residuals|>2) are there?

3. Model interpretation

You have been asked to report what would be the effect on the sales of a territory for every 1 increase in market potential. Report this together with its associated 95% confidence interval to thenearest penny:

Sales would Select increase decrease by (95% CI: to ).

4. Model predictions

The Sales Manager of Fullparts PLC wants to present an award to the salesperson who is responsibile for the 'best' performing territory in the previous financial year. It is decided that the award will go to the salesperson of the territory with the highest observed sales over that which the model predicts.

Complete the following giving the monetary value to thenearest :

The award should go to the salesperson of territory Select A B C D E F G H I J K L M N O P Q R S T U V W X Y for being above the predicted model value.

The Marketing Director of Fullparts PLC has determined that the market potential of territory D has risen from last years value of 35900 to 39500.

Use SPSS to obtain the predicted Sales that this would ensue. Report this together with its associated 95% confidence interval to thenearest :

The predicted Sales for territory D is (95% CI: to ).

For this prediction do you have any reservations due to extrapolation? Select No as the new market potential value falls within the range of last years observed values Yes as the new market potential value is below the minimum of last years observed values Yes as the new market potential value is above the maximum of last years observed values