Interaction Variables
•Suppose that the theory suggests that
advertising is more effective for new
products than for old products.
•Sales = Bo + B1 (adv) + B2 (adv * age) +
error
•Where (adv * age) is an interaction
variable
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Interaction Variables - Applied Regression Analysis - Lecture Slides, Slides of Data Analysis & Statistical Methods
It is the Lecture Slides of Applied Regression Analysis which includes Perfect Multicollinearity, Overall Significance of Equation, Recap, Population of Students etc. Key important points are: Interaction Variables, More Effective, Old Products, Derivate of Sales, Advertising Affects, Evidence For Theory, Hypotheses, Least One, Unrestricted Model, Restricted Model
Typology: Slides
2012/2013
1 / 17
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Interaction Variables
- Suppose that the theory suggests that advertising is more effective for new products than for old products.
- Sales = B (^) o + B 1 (adv) + B 2 (adv * age) + error
- Where (adv * age) is an interaction variable
- Partial derivate of sales with respect to advertising is - d sales /d adv = B 1 + B 2 * age - Which mean that the advertising affects sales depends on the age - To find evidence for theory we should find that B 2 is negative
- How do we set up our hypotheses to test the theory?
Designing your own F test
- Estimate the model with X 1 through X 4 in it (This is your unrestricted model.) find RSS
- Estimate the model with only X 1 and X (^3) in it (This is you restricted model) find RSS
- Which RSS you expect to be higher? Why?
Designing your own F test
- Find the critical F
- Degrees of freedom for numerator = q = number of restrictions
- Degrees of freedom for denominator =n-k-1 (k is the number of independent variables in the unrestricted model)
- Find Fstat = (RSS (^) restricted – RSS (^) unrestricted )/ q divided by RSS unresrticted / n-k-
- If Fstat > F (^) critical reject H (^) o
Chow Test
- Suppose you want to study the relationship between hours of study and grades and you have two samples
- 100 MC students
- 50 Washington State College
- You want to see if it is a good idea to combine the two samples
Chow Test
- Estimate
- (1) GPA = B (^) o + B 1 Study + B 2 SAT + B (^3) Sleep +e (for MC, sample n 1 = 100)
- (2) GPA = B (^) o + B 1 Study + B 2 SAT + B (^3) Sleep +e (for WS, sample n 2 = 50)
- (3) GPA = B (^) o + B 1 Study + B 2 SAT + B (^3) Sleep +e (for MC & WS, sample n 1 + n (^2) = 150)
Non-linear models
- The theory suggest that as Q (quantity of out put) increases, TR (producer’s total revenue) first goes up and then goes down.
fig
0
4
8
12
16
20
0 1 2 3 4 5 6 7
TR
Quantity
TR
TR curve
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How about this model?
- TR = B 0 + B 1 Q 2 + error
- d TR /d Q = 2B 1 Q
- No, Q is either 0 or positive. So, depending on B1, the slope is either positive or negative but not both
How about this one?
- TR = B 0 + B 1 Q + B 2 Q^2 + e
- dTR/d Q = B 1 + 2 B 2 Q
- When Q is zero slope is B 1
- So we expect B 1 to be positive
- We expect B 2 to be negative
- At high levels of Q, the negative component of the slope (2B 2 Q) will greater that the positive component of the slope (B 1 )
- How do you set up the null and alternative hypotheses?
Semi Log Models
- Suppose you want to estimate the percentage growth in a plant as a result of 1 more teaspoon of fertilizer
- ln Size= B 0 + B 1 Fertilizer
- dlnSize/ d Fertilizer = B (^1)
Assignment 7 (40 points) Due: Before 10 PM on Friday October 19
- #4, page 112
- #5, page 112
- Use the data set dvd4 and EViews to test the hypothesis that at high levels of income people are less sensitive to the price of dvd than at low levels of income. Use 5 percent level of significance.
#13, page 113