Name: Date:
Probability and Statistics – Ms. D’AmatoBlock:
Chapter 8 Quiz Review: Linear Regression
Part I: Vocabulary. Using the terms in the word bank, match each term with its correct definition. Each definition will be used only one. Write the correct letter in the space provided.
WORD BANK
A.r2G.Slope
B.InterceptH.Scatterplots
C.Response VariableI.Association
D.ResidualJ.Explanatory Variable
E.CorrelationK.Predicted Value
F.Line of Best Fit / Regression Line
1.The square of the correlation between y and x; the fraction of the variability;
overall measure of how successful the regression is in linearly relating y to x
2.b0; gives the starting value in y-units; it’s the -value when x is 0
3.
4.b1; gives a value in “y-units per x-unit”
5.The value of found for each x-value in the data; the values on the fitted line
6.The difference between data values and the corresponding values predicted by
the regression model; observed value – predicted value
7.Shows the relationship between two quantitative variables
8.Direction, form and strength of a scatterplot
9.Assigned to the y-axis; what you hope to predict or explain
10.Assign to the x-axis; accounts for, explains, or predicts the y-variable
11.A numerical measure of the direction and strength
Part II: Regression Equations. Fill in the missing information in the table below.
12. / / Sx / / Sy / r /a) / 30 / 4 / 18 / 6 / -0.2
b) / 100 / 18 / 60 / 10 / 0.9
c) / 0.8 / 50 / 15 /
d) / 18 / 4 / -0.6 /
Use the space below to show work for completing the table above. Round to the nearest tenth, if necessary.
a) / b)c) / d)
Equations:
Part III: The Regression Line in Real Units.
13.People who responded to a July 2004 Discovery Channel poll named the 10 best roller coasters in the United States. The data that was collected showed the length of the initial drop (in feet) and the duration of the ride (in seconds). A regression to predict duration from drop has r2 = 12.4%.
A]What are the variables and units in this regression?
B]What units does the slope have?
C]Do you think the slope is positive or negative? Explain.
D]Write a sentence (in context) summarizing what the r2 says about this regression.
E]What is the correlation between drop and duration?
14.Consider the roller coasters described in #13. The regression analysis gives the model .
A]Explain what the slope of the line says about how long a roller coaster ride may last and the height of the coaster.
B]A new roller coaster advertises an initial drop of 200 feet. How long would you predict the ride lasts?
15.The SAT is a test often used as a part of an application to college. SAT scores are between 200 and 800but have no units. Before 2005, tests were given in Math and Verbal areas. Doing the SAT-Math problems also involved the ability to read and understand the questions, but could a person’s verbal score be used to predict the math score?
A]For these data, r = 0.685. Interpret this statistic.
B]These verbal scores averaged 596.3, with a standard deviation of 99.5, and the math scores averaged 612.2, with a standard deviation of 96.1. Write the equation of the regression line.
C]Interpret the slope of the line in context to the problem.
D]Predict the math score of a student with a verbal score of 500.
16.Determine whether each statement is TRUE or FALSE.
Correlation has units.
Correlation and regression require explanatory and response variables.
Scatterplots require that both variables be quantitative.
Every piece of data fits onto the line of best fit.
Correlation is between the values of -1 and +1.
17.Classified ads in the Ithaca Journal offered several used Toyota Corollas for sale. Listed below are the ages of the cars and the advertised prices.
Age (yr) / Price Advertised ($)1 / 12995, 10950
2 / 10495
3 / 10995, 10995
4 / 6995, 7990
5 / 8700, 6995
6 / 5990, 4995
9 / 3200, 2250, 3995
11 / 2900, 2995
13 / 1750
A]Make a scatterplot for these data.
B]Describe the association between age and price of a used Corolla.
Direction =
Form =
Strength =
C]What are the explanatory and response variables?
Explanatory Variable =
Response Variable =
D]What is the correlation? Round to the nearest hundredth.
E]What is r2? Round to the nearest hundredth.
F]Find the equation of the regression line and draw it on your graph above. Round to the nearest hundredth.
G]Explain the meaning of the slope of the line in context to the problem.
H]Explain the meaning of the intercept of the line in context to the problem.
I]Explain the meaning of r2 in this context.
J]If you want to sell a 7-year-old Corolla, what price seems appropriate?
K]You have a chance to buy one of two cars. They are about the same age and appear to be in equally good condition. Would you rather buy the one with a positive residual or a negative residual? Explain.
L]You see a “For Sale” sign on a 10-year-old Corolla stating the asking price as $1500. What is the residual? Based on the residual, is this a good buy?
18.Given the table below:
Years since 1996 / Number of participants0 / 68
1 / 73
2 / 83
3 / 81
4 / 86
5 / 94
6 / 96
7 / 103
8 / 114
A]Create a scatter plot.
B]What are the explanatory and response variables?
Explanatory Variable =
Response Variables =
C]Describe the association between years and number of participants.
Direction =
Form =
Strength =
D]What is the correlation? Round to the nearest hundredth.
E]What is r2? Round to the nearest hundredth.
F]Determine the equation of the line of best fit for this data and draw it on your graph above. Round to the nearest hundredth.
G]Explain the meaning of the slope of the line in context to the problem.
H]Explain the meaning of the intercept of the line in context to the problem.
I]Explain the meaning of r2 in this context.
J]If the trend was to continue, what could you predict to be the number of participants in the year 2010?
K]Find the predicted amount of participants for the year 2000 and then use it to find the residual amount.
Predicted amount = Residual =
L]What does the residual amount tell you about the data?
Part IV: Matching. Write the letter of the best description for each graph.
_____19]r = 1, perfect positive correlation_____20] r = -1, perfect negative correlation
_____21]r is near zero and variables are_____22] r is near zero, but the variables are
not related. A horizontal line related through a curvilinear
shows the relation. relation.
_____23] 0 < r < 1, positive correlation._____24] -1 < r < 0, negative correlation.
y increases as x increases. y decreases as x increases.
_____25]r ≈ -0.17_____26]ris near
a) b) c)
d) e) f)
g) h)