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I have a regression model, where I'm attempting to predict Sales based on levels of TV and Radio advertising dollars. The output looks as follows:

enter image description here

I'm using the R predict function to predict the model where TV advertising = 100,000 and Radio = 20,000 (dollars), at a confidence interval of 95%. The call and the output look as follows:

enter image description here

I'm curious about the proper way to interpret this. Is the following correct?

"If the company were to invest 100,000 in TV advertising and 20,000 in Radio advertising, the expected sales would be 8,348 units. And we're 95% confident actual sales units will fall between 7,781 units and 8,915 units."

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Yes, that interpretation is correct. A sanity check:

$2.9211 + 0.04575 . 100,000 + 0.18799 . 20,000 \approx \$8337.7211 $

Presumably, the difference of about $10 in the above estimate can be attributed to the rounding that R does when displaying coefficient estimates.

Reg the interpretation of the confidence interval - The interpretation for the confidence interval would be that there is a 95% probability that the interval we obtained contains the true level of sales at the specified levels of advertising

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  • $\begingroup$ Thank you. I wasn't so concerned about the sales target being exactly right. I was more concerned that I had the concept correct, and,, more importantly, I had the confidence interval interpretation correct. $\endgroup$ Dec 14, 2016 at 19:15
  • $\begingroup$ I think you might be confusing confidence and prediction intervals. The code shows this is a confidence interval, whereas the interpretation in the question reads like a prediction interval. This confidence interval says little about actual sales: it is rather an interval for the mean of the distribution of sales associated with this particular combination of advertising budgets. $\endgroup$
    – whuber
    Dec 14, 2016 at 19:22
  • $\begingroup$ @whuber - Fair enough. So what would an appropriate confidence interval interpretation be? IOW, if you attempted to explain this to your friend who knew little about statistics, how would you word it? $\endgroup$ Dec 14, 2016 at 19:27
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    $\begingroup$ @RandyMinder The interpretation for the confidence interval would be that there is a 95% probability that the interval we obtained contains the true level of sales at the specified levels of advertising. $\endgroup$
    – user142295
    Dec 14, 2016 at 19:42
  • $\begingroup$ @Kant - You should write this up as an answer. I think it's better than the one provided. $\endgroup$ Dec 14, 2016 at 19:56

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