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)
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 Regression Analysis by Example
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 Is the relationship real or just a fluke
Once you run the numbers, you don't just take the result at face value. You check: R-Squared ( R2cap R squared X3cap X sub 3 : Is there a discount running
(Error): The "noise"—factors you didn't measure (like a local parade or a broken espresso machine). 2. Checking the "Goodness of Fit"