### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# BASIC STATISTICS STAT 220

UW

GPA 3.66

### View Full Document

## 41

## 0

## Popular in Course

## Popular in Statistics

This 9 page Class Notes was uploaded by Providenci Mosciski Sr. on Wednesday September 9, 2015. The Class Notes belongs to STAT 220 at University of Washington taught by Staff in Fall. Since its upload, it has received 41 views. For similar materials see /class/192512/stat-220-university-of-washington in Statistics at University of Washington.

## Reviews for BASIC STATISTICS

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/09/15

Chapter 10 Context 2 Regression line 3 Graph of averages 4 Regression estimate 5 6 Example 7 Regression line 8 Graph of averages 9 10 Regression method for individuals 11 Example 12 Method 13 Extrapolation and generalization 14 Percentile ranks 15 Percentile ranks 16 Regression to the mean 17 Regression fallacy 18 Example 19 What is going on 20 21 Regression effect 22 Another explanation 23 Two regression lines 24 25 Context I In chapter 8 we looked at summarizing the relationship between two variables using 0 average of x SD of X 0 average of y SD of y 0 correlation coefficient r I We also looked at the SD line the line that goes through the middle of the football I Now we will discuss another line the regression line I The regression line estimates the average value of y for each value of m Hence it can be used for predicting y from m l Other new terminology regression estimate graph of averages extrapolation regression effect regression fallacy 2 25 Regression line 3 25 Graph of averages Goal we want to describe how one variable depends on the other More precisely we want to estimate the average value of y for a given value of m Example What is the average life expectancy for countries with a GDP of 1 billion USD between 50 and 60 years Example What is the average life expectancy for countries with a GDP of 1 trillion USD between 70 and 80 years 425 Regression estimate We can make such estimates in a more systematic way With an increase of 1 SD in m we do not expect that y increases by a full SD lnstead y is expected to increase by only T SDs This is the regression method and results in a regression estimate 525 Figure 2 Regression method When x goes up by one SD the average value of y only goes up by r SDs y The regression estimate The point of avzr agcs r x SD 2 A 50 x 625 Example I HANES study height and weight of 988 men age 18 24 0 Height average 70 inches SD 3 inches 0 Weight average 162 pounds SD 30 pounds 0 Correlation coefficient 7quot 047 I Estimate the average weight of men that are 73 inches tall I Regression method Step 1 Draw picture Step 2 Convert x to standard units 23 how many SDs are these men above average in height Step 3 Compute 2y Zn gtlt 7quot average weight in standard units 0000 Step 4 Convert 2y back to original units average weight in pounds 7 25 Regression line All the regression estimates fall on one line This line is called the regression line For an increase of 1 SD in x there is an increase of only 7 SDs in y Note that the regression line is always less steep than the SD line because 1 g r g 1 Both the SD line and the regression line go through the point of averages 8 25 Graph of averages The graph of averages shows the average y value for each value of x If the graph of averages follows a straight line it is the same as the regression line If the graph of averages is close to a straight line then the regression line is a smoothed version of the graph of averages l Warning If the graph of averages doesn39t look like a straight line at all then don39t use the regression line 9 25 Figure 3 The graph of averages Shows average weight at each height for the 471 men age 18 24 in the HANESS sample The regression line smooths this graph 270 3 O 2 240 1 O 63 210 20 o D 40 37 C 39 2 Z e 8 10 o v 180 54 68 i I I 59 g 25 29 54 g 150 3 3390 391 17 quot 5 1204 g 2 90 1 58 61 64 67 7O 73 76 79 82 HElGHT lNCHES 10 25 Regression method for individuals 11 25 Example I Math SAT scores and first year GPAs of students 0 SAT score average 550 SD 8O 0 first year GPA average 26 SD 06 O r 04 0 The scatter diagram is football shaped A student is chosen at random Predict hisher first year GPA Our best guess is the average GPA A student is chosen at random and has SAT score 650 Predict herhis first year GPA Our best guess is the average GPA for students with an SAT score of 650 We can find this new average using the regression method 1225 Method I If you know nothing the average is the best guess I If you know the z value the best guess for the y value is the average of the y values for this m You can find this new average using the regression method 1325 Extrapolation and generalization I In SAT example the university has only experience with the students it has admitted Does the regression estimate also work for students who were not admitted Not necessarily but it is often used like that I Be careful with generalizations 0 Sample Does the sample represent the population to which you want to generalize 0 Range The SAT scores in the sample ranged from 400 to 600 The regression method may work poorly for a student with SAT score 200 1425 Percentile ranks l Example SAT scores and first year GPA 0 SAT score average 550 SD 80 0 first year GPA average 26 SD 06 O r 04 0 The scatter diagram is football shaped l A student is chosen at random and is at the 90th percentile of the SAT scores Predict hisher percentile rank on the first year GPA l Method 0 Step 1 Draw a picture 0 Step 2 Find 2m use normal table 0 Step 3 Compute 2y 2m x r 0 Step 4 Convert 2y to percentile rank use norma table 1525 Percentile ranks l Note that we did not use information about average and SD I We only used the normal table and r That is because the whole problem is worked in standard units l Why can we use the normal table Because the scatter diagram is football shaped 16 25 Regression to the mean I Note that the student who was at the 90th percentile for SAT scores was at the 69th percentile for first year GPA scores I So the student was well above average for the SAT and still predicted to be above average for GPA but less so I Why Why don39t we predict the student to be at the 90th percentile I This is because the scores are not perfectly correlated 0 If r 1 then we would predict the percentile ranks to be the same 0 If r 0 then the SAT score does not help us in estimating the GPA so we would predict the percentile rank to be 50 0 If r is between 0 and 1 we predict something in between and the regression method tells us precisely what 17 25 Regression fallacy 18 25 Example I Preschool program for boosting children39s le 0 Children are tested when they enter pre test 0 Children are tested when they leave post test 0 Results I Pre test average 100 SD 15 I Post test average 100 SD 15 I So it seems the program didn39t have much effect I A closer look at the data showed 0 Children who were below average on the pre test had an average gain of 5 IQ points 0 Children who were above average on the pre test had an average loss of about 5 IQ points 1925 What is going on I It seems that the program equalizes intelligence 0 Perhaps the brighter kids play with the dull kids and the difference between the two groups diminishes l Reality not much is going on 0 The children cannot be expected to test exactly the same on both tests 0 These differences make the scatter diagram for the test scores spread around the SD line in a football shape 0 The spread around the line makes that the bottom group comes up and the top group comes down 2025 re 390 tl l cCL li a sun is 1 inch taller than his fat m It an 139 dashed line ints in the su39l 39 2 39 h lt r2 inches all to the o c respond to the farm res u n i fthcs 39 poinb arc below the ted line The points in 0 families it the rather is 04 inches U 03 fthexc points are Above the dashrd line The lid regression line s wit the cenlcrs of all the vertical strips and is atter than the dashed llnCV son39s HEtGHT lNCHESl 2125 Regression effect I Regression effect in almost all testretest situations 0 the bottom group on the first test will on average show some improvement on the second test 0 the top group on the first test will do a bit worse on the second test I Regression fallacy thinking that the regression effect must be due to something important not just spread around the SD line 22 25 Another explanation I Example repeated IQ tests I Basic fact scores will differ a bit due to chance error I If someone did very well on the first test that suggests that heshe was lucky and will probably score a bit lower on the second test I If someone did very badly on the first test then that suggests heshe had a bad day and will probably do a bit better on the second test 23 25 Two regression lines I Two regression lines y on X and X on y I Example IQ scores 9 Women average 100 SD 10 9 Men average 100 SD 10 9 Correlation between IQ of husbands and wives is about 05 I Large study found that men with IQ of 140 had wives whose average IQ was 120 I They also found that women with IQ of 120 had men whose average IQ was 110 I What is going on We talk about different groups of people 24 25 Fig m 9 The two regms on lines wamj g f5 IQ Rgwmimn llr m Fm W husband sva mm w ifmlw 1Q x ngrm man g I llr m for mm I ngwl 39IQ e on g huc banclls IQ Husband39w IQ 25 25

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.