Question

Multivariate analysis

Using the data provided, perform the following analysis:

• Determine the explanatory and response variables.
• Run a multivariate regression analysis on all three variables.

Interpret the results by answering the following questions:

• What is the calculated correlation coefficient? Do the sales figures correlate with the marketing expenditure and price?
• Comment on the coefficient of determination. What percentage of the response data can be explained by the explanatory variables?
• Determine the multiple regression line equation in the form:

sales^ = (intercept) + (coefficient)× marketing + (coefficient)× price

• Using the regression equation formulated, what is the amount of expected sales (in pounds), if the price is set at £3.50 and the amount spent on marketing is £300?
• Interpret the variables in the regression equation. What impact does each of the factors (marketing and price) have on the sales figures?

Total sales	Marketing	Price
£    1,500.00	£       330.00	£           3.50
£    1,354.00	£       270.00	£           3.75
£    1,489.00	£       320.00	£           3.50
£    1,347.00	£       280.00	£           3.90
£    1,321.00	£       260.00	£           4.00
£    1,245.00	£       240.00	£           4.20
£    1,589.00	£       325.00	£           3.50
£    1,632.00	£       340.00	£           3.30
£    1,485.00	£       320.00	£           3.40
£    1,420.00	£       300.00	£           3.70

Answer 1

• here it can be easily seen that sales is response variable and marketing and price are explanatory variables as marketing and price of a product effects it's price.

• Let X1 represent marketing value , X2 represent price value, and y represent sales value:

the regression equation is:

calculation:

• Let X represent given sales value and Y represent predicted sales value:

this is a strong relation i.e. sales figure strongly corelate with marketing and price values.

• 

91% response data can be explained by explanatory variables.

• for X1= 300 , X2= 3.5, Y= 2.68774*300- 94.24231*3.15 + 982.25099 = 1458.724

• with increase in marketing value, sales increase since it's coefficient is positive whereas with increase price value, sales decrease since it's coefficient is negative.