THE SAT ESSAY: IS LONGER BETTER?  In March of 2005, Dr. Perelmen from MIT reported, “It appeared to me that regardless of what a student wrote, the longer the essay, the higher the score. If you just graded them based on length without ever reading them, you’d be right over 90% or the time.” Analyze the data and use it to respond to Dr. Perelmen’s claim.

WordsScoreWordsScoreWordsScoreWordsScore

LSRL –Least Squares Regression Line O The line that minimizes the distance from each data point to the linear model.

O Model for the data O Helps us predict y given an x value. LSRL –Least Squares Regression Line

NEA change (cal) Fat Gain (kg) Does Fidgeting Keep You Slim? NEA change (cal) Fat Gain (kg) (NEA) Non-Exercise Activity

O Find the regression line.

O Interpret each value (y-int & slope) in context.

O Predict: if NEA increases to 400 calories, what will the fat gain be? O What about if NEA increases to 1500 cal?

O Interpolation – the use of a regression line for prediction within the interval of values of explanatory variable x. O A good predictor. O Extrapolation – the use of a regression line for prediction far outside the interval of values of explanatory variable x. O Often not accurate

Example 2

Residuals O The difference between an observed value of response variable and value predicted by the regression line..

Residuals o Negative residual means the model OVER PREDICTS the y value. o Positive residual means the model UNDER PREDICTS the y value.

Example 3 NEA change (cal) Fat Gain (kg) NEA change (cal) Fat Gain (kg)

EXIT TICKET  Write down the LSRL for the SAT question.  Describe the slope in context of the data.  Describe the y-intercept in context of the data. Explain why it doesn’t make sense.  Predict what your score would be if you wrote 300 words. How about 700 words?