A study was conducted to relate the advertising expenditure (in million of dolla

Question

A study was conducted to relate the advertising expenditure (in million of dollars) of 21 firms and advertising impressions retained per week by the viewers of the products of these firms (in millions). Letting Y represent advertising impressions retained and X the advertising expenditure, the following regressions were obtained: Model I Yˆi = 22.163 +0.3631Xi se = (7.978) (0.0971) R2 = 0.283 Model II Yˆ = 7.059 + 1.847Xi 0.0040X2 i se = (9.986) (0.3699) (0.0019) R2 = 0.53

(a) Interpret both models.

(b) Which is a better model? Why?

(c) Which statistical test(s) would you use to choose between the two models?

(d) Are there “diminishing returns” to advertising expenditure, that is, after a certain level of advertising expenditure (the saturation level), does it not pay to advertise? Can you find out what is a good level of expenditure? Explain your answer.

Explanation / Answer

A) we have use only one variable here for Model1 and we get R2 as 0.283

But using two covariates in model 2 we get R2 as 0.53 so adding one variable in model 2 it gives sufficiently good result.

B) since R2 value of model 2 is significantly higher than the Model1 so model 2 is better than the model1

C) to test for which model is good go for goodness of fit test that gives chi-square test.

If both the model gives significantly gits to the data then which test gives lower P-value is the good model.

If one rejects and one accepts null hypothesis then the model rejects null hypothesis is the good one.

D) yes. As because in model 2 we have entered X^2 that has the negative coefficient so increment of X^2 gives negative effect to Y

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