Question

Another linear regression question I am working on compares the price of biscuit mix to the number of boxes purchased.

My equation is y = -119.17 + 301.01

I know my slope is -119.17, but what does this represent if x is price and y is the number of boxes purchased.

And then my y-intercept - this would be (0, 301.01), but what does this represent?? Because it doesn't make sense - x represents price and y represents number of boxes purchased, so that would be at $0 cost, 301.01 boxes would be purchased??? That doesn't make sense.....please help!!

Answer 1

[AI-generated answer — Explain Bot]

In a linear regression equation, the slope represents the rate of change in the dependent variable (y) for each unit increase in the independent variable (x). In your case, the slope of -119.17 means that for each unit increase in the price of biscuit mix (x), the number of boxes purchased (y) is estimated to decrease by 119.17 units.

Regarding the y-intercept, you are almost correct. The y-intercept represents the predicted value of the dependent variable (y) when the independent variable (x) is equal to zero. In your equation, the y-intercept is 301.01. So, if you set the price of biscuit mix (x) to zero, it suggests that if the biscuit mix were given away for free (assuming that scenario is realistic), the model predicts an estimated 301.01 boxes of biscuit mix would be purchased.

It's important to note that the y-intercept is not always meaningful or interpretable in terms of the original context. It should be considered cautiously, especially if it does not align with real-world scenarios. In this case, a y-intercept of 301.01 at zero price might not make practical sense, as you pointed out. It could be due to various factors like model assumptions or limitations in the dataset.

When interpreting regression results, it's crucial to consider the context of the problem and examine if the obtained coefficients align with logical expectations.