Suppose you are consulting for a cereal brand that ran a media campaign over 8-w

Question

Suppose you are consulting for a cereal brand that ran a media campaign over 8-weeks back in 2016. You have collected their sales data and ran the following model:

where WeeklySales are store-level weekly sales of this cereal product, $

TVSpend is TV ad spend per week during this ad campaign, $

PressSpend is Press ad spend per week during this ad campaign, $.

Suppose after you run your model you get the following output

Estimate Std. Error

(Intercept) 1000.434262 0.235423

TVspend 4.84090 0.001600

PRESSspend -1.34455 0.768899

a. Interpret coefficients on Intercept, TVSpend and PressSpend. Do they make sense?

b. Derive 95% confidence intervals for these variables, assuming large sample size. What is the economic meaning of these confidence intervals? How should we interpret them back to the cereal brand management?

c. What could have caused a negative PressSpend variable? How might it affect other coefficients in the model? Explain.

4. Suppose you are consulting Eor s cereal brand that ran s nedis espai on over 8-Yeeks back in 2016. You have eolleeted their sales d s and ran the following n Weekly Sales ntercept +B1TVSpend +B2Press Spend u where v ellysales are store level weekly sales of this real produot, Tyspend is TV ad spend per week during this ad ompaion Press Spend is Press ad spend per veek dur ne this ad oonpai Suppose after you run your nodel you eet the followine output Estinate Std, Error (Intercept) 000, 434282 0.235423 Ivspend 4.84090 0.001600 -1.3ME5 ERESSspend 0.768899 a Interpret ffi on Inte TVSpend and F Spend. Do they Take sense? b. Derive 95s confidence inter als for these wariables, assunine larte sangle sire. What is the econonic nesnine of these confi dence inter als? H should ve interpret then back to the cereal brand nanate ent? e Nhst ee hav sused a negative PressSpend variable? How night it sffeet other coeffi in the nod Exp ould

Explanation / Answer

Sol:

a:

weekly sales=1000.434262+4.84090(TV spend)-1.34455(PRESSspend)

B0, the Y-intercept=1000.434262, can be interpreted as the value you would predict for weekly sales if both TV spend= 0 and PRESSspend = 0.

"If PRESSspend is fixed, then for each change of 1 unit in TVspend , weekly sales changes 4.84090 units."

"If TVspend is fixed, then for each change of 1 unit in PRESSspend , weekly sales changes 1.34455 units."

Soutionc

negative indicates indirect relationship

that is weekjly sales increase if pressspend decreases and viceversa

Solutionb:

To construct confidence interval:

:

For TV spend

sample statistic=4.84090

confidence interval 95%

critical value=1.96 for 95% cconfidence interval

magin of error=critical value*std error

=1.96*0.001600

=0.003136

95% CI for Tv Spend=

4.84090-0.003136,4.84090+0.003136

4.837764,4.844036

lower limit=4.837764

upper limit=4.844036

Similarly PRESSspend

Sample statistic= -1.34455

95% CI for PRESSspend =-1.34455-1.96*0.768899,-1.34455+1.96*0.768899

=-2.8516,0.16249

lower limit=-2.8516

upper limit=0.16249

. You can be 95% confident that the real, underlying value of the coefficient that you are estimating falls somewhere in that 95% confidence interval,

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