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**Unformatted text preview: **h Stat 201 - Exam 2 - Topics List- Spring 2010 My answers/thoughts to her guide are in italics. If there's any incorrect information, email me at cbelford@utk.edu Chapter 8: Linear Regression Four conditions for valid regression o Quantitative variables ... does not work for categorical data o Straight-enough condition... Ensure linearity, meaning they have an association/correlation. Lower p-values indicate better lines; higher R squared indicate better lines. o Outlier condition... make sure outliers don't have a'1Y influence(change the fit line noticeably) or leverage(significant 'x' value difference) on the fit line o "Does the plot thicken?" condition Not referenced a lot in the slides, but there is an inference that states the purpose is to check the residuals to back up your original conclusions from the scatterplot What is special about the regression ("least squares") line compared to any other line drawn through the data o The "least squares" line is special because the sum of all the residuals will add to zero (or as close as possible) Given JMP output, write out the regression model with actual variable names o For example, fat(!')= 6.8 + .97 *protein, is the model, so you're answer would be: For every gram of protein, the model says you'll have . 97 additional grams of fat. It also states that when there is 0 grams of protein, you'll have 6.8 grams of fat. Interpret regression coefficients (bO and b l) o Using the formula above, y(! ' ) = b(O) + b(l) * x, you can see that b(O) is they-intercept and b(l) is the slope of the regression model. Know when bO has no logical interpretation o For example, GasMileage = 4.2 + 2.87 * FuelAdditive(mL). You could say that for every additional mL of fuel additive, you'll get an additional2.87 mpg; however, would it make sense to say that you only get 4.2mpg with no fuel additive?...the model I've used is completely made up, but the idea is the same as long as the numbers don't reflect a possible scenario. Know the difference between y andy-hat o Actual observed values= y; predicted values= y(!'), or y-hat Be able to use a regression equation to make an estimate of y for a given value of x o In the fat & protein regression model, let's say we're told a sandwich has lOg of protein. Thereforey = 6.8 + .97 * 10 =16.5. According to this regression model, we believe a sandwich with lOg of protein will have 16.5g of fat. Be able to calculate and interpret a residual o Residuals are calculated by subtracting the the actual value from the predicted value, or y y( A ). If the residual is positive, it is said the model underestimated the value. If the residual is negative, it is said the model overestimated the value....

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