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Wednesday, July 20, 2011

Multiple Regression

Bob enjoyed our extended definitions so much that I thought I’d try another one.

Regression analysis may seem initially daunting, but the logic is really quite simple when you breakdown the technical terms into language you can understand.

Multiple regression is used to study the correlation between two or more predictor variables and one criterion variable. It measures the impact of several independent variables on the dependent variable. Basically, it helps to answer the question, “What is the affect of this on that?”


Y = a + b1X1 + b2X2 + ... + bpXp

Y = dependent variable = QD = Quantity Demanded

a = constant or Y intercept

X = independent variable = the variable affecting change in the dependent variable Y

b = coefficient of the X variable = measures the impact of the independent variable X on the dependent variable Y


Inserting values into the equation:

Y = Class enrolment at KPU = ?

a = Minimum class size = 17

X1 = Cost of tuition at KPU = 4 (ie. $4,000)

X2 = Cost of tuition at SFU = 5 (ie. $5,000)

X3 = Advertising/Promotion = 5 (ie. $5000)


Then, Y = a + b1X1 + b2X2 + ... + bpXp becomes:

QD = 17 – 13(4) + 10(5) + 4(5)

From this equation, we can determine QD = Enrolment at KPU = 35 students.


17

This value refers to the constant, or Y intercept. It can be considered the fixed value. Here, it represents the minimum class size at KPU of 17 students.

-13(4)

The operator (negative here) denotes an inverse relationship between the cost of tuition at KPU and student enrolment at KPU. This is also an indication that these two variables complement each other and move in the opposite direction. This means that a unit change (increase) in the cost of tuition at KPU ($1,000) will cause the student enrolment at KPU to decrease by 13 students. In other words, higher tuition means fewer students can afford to enrol. On the other hand, if tuition cost were to fall, enrolment would increase.

+10(5)

The positive operator indicates a direct relationship between the cost of tuition at SFU and student enrolment at KPU. The universities act as substitutes for one another, and the variables move in the same direction. This means that a unit change (increase) in the cost of tuition at SFU ($1,000) will cause the student enrolment at KPU to increase by 10 students. Likewise, if tuition were to decrease at SFU, more students would forgo attending KPU for SFU.

+4(5)

Similar to SFU tuition costs mentioned above, the positive operator denotes a direct relationship between the advertising budget and student enrolment at KPU. This indicates that student enrolment is influenced by the amount of money that Kwantlen spends in advertising the university. Here, it means that for each unit change in the advertising budget for KPU ($1,000), student enrolment at KPU will change by 4 students in the same direction.

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