Question

Question: In a small scale market study investigating brand liking (Y) for product variations with differen...

In a small scale market study investigating brand liking (Y) for product variations with different moisture content (X₁) and sweetness (X₂), the following data were obtained.

Product Variation	Moisture Content	Sweetness	Liking
1	4	2	64
2	4	4	73
3	4	2	61
4	4	4	76
5	6	2	72
6	6	4	80
7	6	2	71
8	6	4	83
9	8	2	83
10	8	4	89
11	8	2	86
12	8	4	93
13	10	2	88
14	10	4	95
15	10	2	94
16	10	4	100

Problem: Regress Liking on each of the other two factors independently. Regress Liking on both of the two other factors simultaneously. Discuss results. Based on the multiple regression, what would the expected liking for a product variation that includes 7 moisture content and 5 sweetness? Is this a valid expectation? Why or why not?

Answer 1

We have analyzed the data provided using the regression feature from Microsoft Excel (Available in the data analysis section).

The result of moisture as independent factor is shown below.

In the results, the key statistics that we need to look at is the R square value. This value varies from 0 to 1 and the close it is to 1 it shows a higher degree of impact on the dependent variable.

In addition to this we should also look at the standard error value. The lower this value, the better suited is the regression line.

Based on the result we can see that the R square value of multiple regression is 0.94. This makes it an extremely good model to predict the likely dependent variable. On the other hand the simple linear regression on individual factors show values of 079 and 015 for Moisture and Sweetness respectively. This shows that Moisture has more role to play than sweetness in the king of the product.

In addition we see that the standard error of multiple regression is much lower at the value of 269. Thus the fitment of regression line drawn from the multiple regression equation is good.

The equation that we can make from these results is (rounding to 1 decimal place)

Y = 37.6 + 4.4 X1+ 42 X2

With this equation we can predict the liking for 7 moisture content and 5 sweetness. It will be

Y=37.6 + 44*7 +4.3*5= 89.9

This is a valid expectation as the R square value is high and the standard error of the regression is low. We can expect the actual result to be very close to this value.