# Use regression model results to estimate change in dependent variable

A dataset consists of sales of a product in different regions alongside advertising budget in three different media: Radio, Instagram, Facebook. A model is developed to predict sales on the basis of three media budgets. The model coefficients are as follows

Coefficient Std Error p-value1
Intercept 3.365 0.3119 0.000105
Instagram 0.06 0.0041 0.78

If the company decided to shift \\$1000 marketing spend from Facebook to Radio. How much sales increase/decrease can you expect approximately? a)$294

b) $299 c)$352

d) \$235

The question appeared on a test as is. I am trying to understand how we can actually calculate the effect and or/ how to guess the right option?

• Welcome to Cross Validated! We have a particular way we handle self-study questions like this. What progress have you made with this problem?
– Dave
Commented Oct 7, 2021 at 21:28
• I have checked the stats books I have and online but have not found a similar question. From what I understand I know what the p-value, the std error means the margin of error, and the coefficient value is 'm' in the 'y=mx+c' equation for linear regression. Intercept represents the mean value of y when x =0. @Dave Commented Oct 7, 2021 at 21:33

This question has a lot of details but it's actually quite simple. It only requires you to separate the wheat from the chaff. Recall that $$E[y|x]=\beta^Tx$$, that's all you need here.
Let the vector of initial budgets be $$x=(x_r,x_i,x_f)$$ and the expected sales $$E[y|x]=3.365+0.294x_r+0.06x_i+0.059x_f$$ Now we've shifted 1000 from facebook to radio so our budget vector is now $$x'=(x_r+1000,x_i,x_f-1000)$$. The expected sales are
$$E[y|x']=3.365+0.294(x_r+1000)+0.06x_i+0.059(x_f-1000)\\=3.365+0.294x_r+294+0.06x_i+0.059x_f-59\\=3.365+0.294x_r+0.06x_i+0.059x_f+294-59\\=E[y|x]+235$$