Quiz 9 Review Name:
Standard(s) assessed / Score2. Correlation Coefficient
· Calculate and interpret the correlation coefficient
3. Calculate and Apply Regression Equation
· Calculate the regression equation
· Graph and make predictions based on the LSR line
· Understand the difference between an outlier and an influential observation in the context of regression – level 1 only
4. Interpret Regression Equation
· Interpret the slope and intercept of the regression equation
· Understand the Least Squares criterion for line of best fit
1. 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) students at this school are underachieving.
(c) the exam is a poor predictor of success.
(d) students who do best on this exam will make the worst students.
(e) someone has made a mistake
2. Circle the correct answer:
If a correlation coefficient between the number of songs stored in someone’s iPod and the number of shoes a person has in their closet is 0.80, then:
(a) The more shoes a person owns, the fewer songs they have
(b) The more songs the person has, the more shoes they have
(c) how many shoes a person has does not have anything to do with how many songs they have
(d) buying shoes causes people to download more songs
3. Circle the correct answer:
(a) The closer a correlation coefficient is to 1, the more evidence there is of a causal relationship between the explanatory variable and the response variable.
(b) The closer a correlation coefficient is to 0, the more evidence there is of a causal relationship between the explanatory variable and the response variable.
(c) The closer the value of r is to -1, the more evidence there is of a causal relationship between the explanatory variable and the response variable.
(d) It is never appropriate to draw conclusions about causality based on a correlation alone.
4. The following scatterplot is based on ratings of different wines. Which is the best estimate of the correlation between oakiness and quality?
(a) -.05
(b) .55
(c) .99
(d) -.55
X / 4 / 2 / 8 / 6 / 10 / 6Y / 8 / 4 / 18 / 22 / 30 / 8
5. Suppose one collected the following information where X is diameter of tree trunk and Y is tree height.
If the Regression equation is y = -3.6 + 3.1x , what is your estimate of the average height of all trees having a trunk diameter of 7 inches?
(a) 20.1 (c) 22.1 (e) 19.1
(b) 18.1 (d) 21.1
6. The “line of best fit” under the least squares criterion is the one which…
(a) minimizes the sum of the perpendicular distances from the points to the line.
(b) has the least sum of squared errors in predictions.
(c) has the smallest residual correlation.
(d) makes the standard deviation of the residuals as large as possible.
(e) None of the above
Use the following StatCrunch output for data collected on the cost (in cents per 3 table spoons) and quality rating for various brands of peanut butter to answer questions 7-9
Simple linear regression results:
Dependent Variable: Cost
Independent Variable: Quality
Cost = 12.40263 + 0.17016451 Quality
Sample size: 37
R (correlation coefficient) = 0.5077
R-sq = 0.25779432
Estimate of error standard deviation: 5.6028185
7. Predict the cost of a peanut butter brand with a quality rating of 60
(a) 10.3 cents
(b) 14.5 cents
(c) 18.1 cents
(d) 22.6 cents
8. Which of the following is the best interpretation of the slope of the regression line?
(a) An increase in 1 quality point is associated with an increase in cost of 17 cents.
(b) An increase in 1 quality point is associated with an increase in cost of 12.4 cents.
(c) An increase in cost of 1 cent is associated with an increase in quality by 12.4 points
(d) An increase in cost of 12.4 cents is associated with an increase quality by .17 points
9. Which of the following is true?
(a) The slope of the regression line is .17
(b) Peanut butters of higher quality have higher costs
(c) Peanut butters with low cost have lower quality
(d) All of the above