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# lec10 - STATISTICS 13 STATISTICS Lecture 10 Oct 18 2010...

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STATISTICS 13 STATISTICS 13 STATISTICS 13 Lecture 10 Lecture 10 Oct. 18, 2010 Oct. 18, 2010

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Review Correlation coefficient Linear regression Formula x b y a s s r b bx a y x y ,
Interpretation of Regression Results The regression line for y on x estimates the average value for y corresponding to each value of x and can be used for prediction With each increase of one SD in x there is an increase of only r SDs in y, on the average. The point is always on the fitted regression line Example: “Booking vs. Hotel Occupancy” . You are told that there are 70 thousands passengers and asked to predict the occupancy rate. ) , ( y x

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Example: HANES Health and Nutrition Examination Survey (from Statistics by Freedman, Pisani and Purves): Data: heights and weights of 988 men age 18- 24 The scatter plot is football shaped.
Example: HANES (cont.) Summary of Data: -average height=70in, SD=3 in -average weight=162p, SD=30 p -r=0.47 Question : suppose one of these men is picked at random, and you have to guess his weight without being told anything about him, what would be your guess? How about if you are told the man’s height: 73 in, what would be your guess then? Answer:

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Regression Effect Example in first day: A preschool program attempts to boost children’s IQ. The children are tested when they enter the program , and again when they leave. On both occasions, the average score is nearly 100. The program seems to have no effect. However, a closer look at the data shows that the children who were below average on the pre-test had an average gain of about 5 points, and those children who were above average on the pre-test had an average loss of about 5 points. Does the program operate to equalize intelligence?
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