A company wishes to understand how sales are influenced by the price of its product. To do this, the company randomly chooses 12 UK cities and offers the product at different prices. The result are shown in the table below:
City Price (£) Sales London 2.24 100 Birmingham 4.63 88 Manchester 3.41 94 Derby 3.54 84 Edinburgh 6.22 56 Glasgow 7.12 49 Cardiff 4.76 76 Belfast 7.52 34 Portsmouth 4.21 79 Bristol 6.29 46 Leicester 4.92 80 Newcastle 5.17 63
1. Conduct linear regression analysis.
• Perform, using Excel, Data Analysis Pack, Regression function, the regression analysis.
2. Produce the scatterplot including a fitted regression line.
3. Write the regression equation using the results of the excel table.
4. Determine & interpret the slope.
5. Determine & interpret the intercept.
6. Determine and interpret the R-Squared value?
7. Give predictions for volume of sales when the price of the product is set to:
a. £3.50 [3 marks] b. £5.80 [3 marks]
8. Explain why the predicted sales volume in question 7. above is just an estimate
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Regression analysis is the technique which is widely used for prediction and forecasting. It is basically used to know that dependent variable is related to which independent variable. Linear regression is used to estimate the relationships between variables by fitting an equation to given data. Linear Regression is used to predict the value of y which is dependent on x (explanatory variable or independent). If we consider one independent variable it is referred to as Linear Regression. While if we consider more than one independent variable it is referred to as Multiple Linear Regression models.
The equation of Linear Regression is
With a unit increase in Xi there is βi unit increase/decrease in Y
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