Chapter 11 review Stats

Practice Problem 3

1. -0.33 2. m = -0.33/1 As the weight increases by one 100 pound we expect to see a -0.33 decrease in fuel economy 3. 28.67 4. 30.32

Practice problems 1

1. Negative linear 2. yhat=38.45-.09*x 3. r=-0.88 (double check this on recorded lecture) 4. m= -0.09 5. m= -0.09/1 for every one Unit increase in horse power we expect a 0.09 decrease in MPG 6. yhat= 38.45-0.09*280 = 13.25 MPG 7. residuals = observed - predicted Yes, I can determine predicted using the regression equation. And I was given the observed 8. yhat=38.45-0.09*170 = 23.15 Residual = 18-13.35 =-5.15 MPG

Practice problem 2

1. negative linear 2. yhat= 560.65 -3.08*x 3. r = square root(rsquare) = SQuare root(0.421)= -0.65 4. m = -3.08 5. m = -3.08/1 For every one minute increase at the table we predict a 3.08 decrease in calories eaten 6. yhat=560.65-3.08*25=483.65 7. yhat=560-65-3.08*41=434.37 8. risiduals=observed-predicted. we can find the predicted from the regression equation. We do not have the observed, so we cant find the residuals

Practice problem 4

1. square root of rsquard= correlation coefficient 0.808 2. yhat=11.036+0.823x 3. m = 0.823 4. For every one percentage increase in reading we can expect to see a 0.823% increase in math proficiency 5. yhat=11.036+.823*69 = 67.823%

Practice Problem 5

1. square root of rsquared =0.90 2. yhat=160.194+.10*x 3. 0.10 1000's of dollars 4. 0..10/1 For every 1 square foot increase we expect to see an increase of 0.10 1000s of dollars 5. 440.19 1000s of dollars 6. 465.09 1000s of dollars 7. look at lecture for this 8. no, its beyond the maximum x values that we have

Scatterplot

A scatterplot is simply a graph in which you plot the ordered pairs. • A scatterplot is a graph of the ordered pairs for data collected on two quantitative variables. • Scatterplots allow us to see if there is an association between the two variables • In other words, whether there is a pattern to how the variables change in relation to each other. • We will plot the data as ordered pairs (x,y) using an x-y axis for the display. • The two axes can represent different units. • Be sure to clearly label the axis so that it is clear what variable and units are used on each axis.

If the class mean was 83.5% and the class median is 90%, is the histogram of the data likely to be:

Left Skewed

Residual practice slide

STARTS ON SLIDE 49

Prediction

The first thing that you need to do is to enter your values into the calculator. • To do this go to STAT>EDIT and enter your explanatory variable (x) in L1 and your response variable (y) in L2. Then press Stat and 8 Then l1 , l2 (x,y) NOT WORKING ON MY CALC NEED TO ASK TEACHER WHAT IS WRONG

ON QUIZZES AND TESTS Practice • Example: Several scatterplots are given with calculated correlations. Which is which? • Correlations: a) -0.944, b) -0.435, c) 0.004, d) 0.753

This shows 2 negatives and 2 positives so match them up The closer to plus 1 or -1 the tighter the correlation

Practice • Let's practice this one more time using a smaller dataset. This time let's visit Burger King and select a few of their lunch items. • Now use your calculator to obtain the regression equation. • 𝒚 = 𝟗.21 + 𝟎.𝟔𝟔x

USE SLIDE 43 FOR THIS 9.21+.66x35 = 42.21 9.21+.66x35 = 32.31

Diameter is regression

age is the explanitory

Residuals = observed - predicted NEED TO KNOW FOR TEST

residual is difference between observed value - predicted value

Interpreting the slope NEED TO KNOW FOR TEST

slide 51

How to graph scatterplot

stat calc go to option 8 enter enter

Examples of Scatterplot

• Example: • Number of hours studying for a test, grade on the test • Number of hours studying for a test, problems missed on the test • Example: The accompanying table lists the weights (in hundreds of pounds) and highway fuel usage rate (mi/gal) for a sample of domestic new cars. Based on the result, can you expect to pay more for gas if you buy a heavier car? • Which variable seems to "explain" the outcome of the other? • So _ weight _______ is the explanatory variable • and __ fuel usage rate _ is the response variable for this problem.

Variables:

• The variable for the x-axis is called the predictor or explanatory variable. This is the variable that we control or manipulate. • The variable for the y-axis is called the response variable. It is the variable that we are studying to see how it reacts.