By Example: Regression Analysis

(Error): The "noise"—factors you didn't measure (like a local parade or a broken espresso machine). 2. Checking the "Goodness of Fit"

Is the relationship real or just a fluke? A p-value under 0.05 generally means your result is statistically significant. 3. Adding Complexity (Multiple Regression) Temperature isn't the only factor. You might add: X2cap X sub 2 : Is it a weekend? (0 for no, 1 for yes). X3cap X sub 3 : Is there a discount running?Now your model looks like: 4. The "Golden Rules" (Assumptions) Regression Analysis by Example

Regression isn't just about the past; it’s about the . With a solid model, you can check tomorrow's weather forecast and know exactly how much milk to order. (Error): The "noise"—factors you didn't measure (like a

Y=β0+β1X+ϵcap Y equals beta sub 0 plus beta sub 1 cap X plus epsilon β0beta sub 0 (Intercept): Sales when the temperature is 0 degrees. β1beta sub 1 A p-value under 0

Your prediction errors are consistent (you aren't way more "off" on hot days than cold days). Normality: The errors follow a bell curve. Why this matters

(Slope): For every 1-degree increase in temperature, how many more coffees do you sell?

): This tells you what percentage of the "story" is explained by temperature. If , then 85% of your sales fluctuations are due to heat.