AP Statistics Review for Chapter 3 Test



_________ 1. We are interested in finding the linear relation between the number of widgets purchased at one time and the cost per widget. The following data has been obtained:

|Number of widgets purchased (x) |1 |3 |6 |10 |15 |

|Cost per widget in dollars (y) |55 |52 |46 |32 |25 |

Suppose the regression line is = -2.5 x + 60. We compute the cost per widget if 30 are purchased and observe:

a. = -15 dollars; Obviously, we are mistaken. is actually +15 dollars.

B = 15 dollars, which seems reasonable judging by the data.

c. = -15 dollars, which is obvious nonsense. The regression line must be incorrect.

d. = - -15 dollars, which is obvious nonsense. This reminds us that predicting y outside the range of x values in our data is a problem.

_________ 2. A researcher finds that the correlation between the personality traits "greed" and "superciliousness" is -.40. What percentage of the variation in greed can be explained by the relationship with superciliousness?

a. 60% b. 0% c. 16% d. 20% e. 40%

_________ 3. Which of the following values of r indicates the most accurate prediction of one variable from another?

a. r = 1.18 b. r = -.77 c. r = .68

_________ 4. If the correlation between age of an auto and money spent for repairs is +.90, then

a. 81% of the variation in the money spent for repairs is explained by the age of the auto.

b. 81% of the money spent for repairs is unexplained by the age of the auto.

c. 90% of the money spent for repairs is explained by the age of the auto.

d. None of the above.

_________ 5. If the coefficient of correlation equals .61, it indicates that the proportion of the variation in

the dependent variable explained by the variation in the independent variable is

a. 37% b. 61% c. 98% d. cannot be determined

_________ 6. True or False? Justify your answer.

The coefficient of determination can have values between -1 and +1.

_________ 7.We are interested in finding the linear relation between the number of widgets purchased

at one time and the cost per widget. The following data has been obtained:

|Number of widgets purchased (x) |1 |3 |6 |10 |15 |

|Cost per widget in dollars (y) |55 |52 |46 |32 |25 |

Suppose the correlation between x and y is -.95. Which of the following conclusions is correct?

a. The linear relation between x and y is weak, and y decreases when x increases.

b. The linear relation between x and y is strong, and y decreases when x increases.

c. The linear relation between x and y is strong, and y increases when x increases.

d. The linear relation between x and y is weak, and y increases when x increases.

_________ 8. Consider a sample least squares regression analysis between a dependent variable (y) and

an independent variable (x). A sample correlation coefficient of -1 tells us that:

a. There is no relationship between y and x in the sample

b. There is no relationship between y and x in the population.

c. There is a perfect negative relationship between y and x in the population.

d. There is a perfect negative relationship between y and x in the sample.

_________ 9. The correlation between anxiety and performance on complex tasks is -0.73. Which of the

following may be concluded?

a. As anxiety increases, performance on complex tasks improves.

b. As performance on complex tasks improves, anxiety tends to decrease.

c. High levels of anxiety cause poor performance on complex tasks.

d. As anxiety decreases, so does performance.

_________ 10. If we obtain a negative r (Pearson r correlation coefficient) this means that :

a. Individuals scoring high on one variable tend to score low on the other variable.

b. Individuals scoring high on one variable tend to score high on the other variable.

c. There is no relationship between the two variables.

d. We have made an error.

_________ 11. A correlation between college entrance exam grades and scholastic achievement was

found to be -1.08. On the basis of this you would tell the university that:

a. The entrance exam is a good predictor of success.

b. They should hire a new statistician.

c. The exam is a poor predictor of success.

d. Students at this school are underachieving.

_________ 12. The correlation coefficient for x and y is known to be zero. We can conclude that:

a. x and y have standard distributions.

b. The variances of x and y are equal.

c. There exists no relationship between x and y.

d. None of these

_________ 13. In a study to determine the relationship between two variables, a coefficient of

determination of -.90 was obtained. This indicates that

a. The computations are wrong since r cannot be negative.

b. There is a fairly low relationship between the two variables.

c. The coefficient of determination is the square root of .90.

d. None of these

_________ 14. A coefficient of correlation of -.80

a. Is lower than r = +.80.

b. Indicates the same degree of relationship as r = +.80.

c. Is higher than r = +.80.

d. No comparison can be made between r = -.80 and r = +.80.

_________ 15. The sign (plus or minus of a correlation coefficient indicates

a. The direction of the relationship.

b. The practical importance of the relationship.

c. The probability that the degree of relationship is greater than zero.

d. The statistical significance of the relationship.

Part 2: Solve the following problems. Make sure you answer the question asked.

1. The Franklin National Bank failed in 1974. Franklin was one of the 20 largest banks in the nation, and the largest ever to fail. Could Franklin's weakened condition have been detected in advance by simple data analysis? The table below gives the total assets (in billions of dollars) and net income (in millions of dollars for the 20 largest banks in 1973, the year before Franklin failed. Franklin is bank number 19.

Bank |1 |2 |3 |4 |5 |6 |7 |8 |9 |10 | |Assets |49.0 |42.3 |36.3 |16.4 |14.9 |14.2 |13.5 |13.4 |13.2 |11.8 | |Income |218.8 |265.6 |170.9 |85.9 |88.1 |63.6 |96.9 |60.9 |144.2 |53.6 | |

Bank |11 |12 |13 |14 |15 |16 |17 |18 |19 |20 | |Assets |11.6 |9.5 |9.4 |7.5 |7.2 |6.7 |6.0 |4.6 |3.8 |3.4 | |Income |42.9 |32.4 |68.3 |48.6 |32.2 |42.7 |28.9 |40.7 |13.8 |22.2 | |

a. We expect banks with more assets to earn higher income. Make a scatterplot of these data that displays the relation between assets and income. Mark Franklin (Bank 19) with a separate symbol.

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b. Describe the overall pattern of your plot. Are there

any banks with unusually high or low income relative to their assets? Does Franklin stand out from other banks in your plot?

c. Find the Least-Squares Regression Line for predicting a bank's income from its assets. Draw the regression line on your scatterplot. Show your calculation for slope and y-int

Assets [in billions]

e. Write a sentence each in the context of the problem for the slope, y-intercept, coefficient of correlation (r), and coefficient of determination (r2)

f. Use the regression line to predict Franklin's income. Was the actual income higher or lower than predicted?

g. In the space below, show the calculation of the residual for the first data point. Make a Residual Plot on the grid below. Are there any outliers or influential points?

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Income in millions of $

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