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m2-09

# m2-09 - STOR 155 Section 2 Midterm Exam 2 Name PID...

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Page 1 STOR 155 Section 2 Midterm Exam 2 (11/10/09) Name: ______________________________ PID: ________________________________ Instructions: Both the exam and the bubble sheet will be collected. On the bubble sheet, print your name and ID number, sign the honor pledge, also bubble in your name and ID number. Each question has only one correct choice (decimals may need rounding). Use #2 pencil only (do not use ink) to fill bubble completely. No notes or remarks are accepted. Do not tear or fold the bubble sheet. A grade zero will be assigned for the entire exam if the bubble sheet is not filled out according to the above instructions. Use the following to answer questions 1 -- 2: Many high school students take either the SAT or the ACT. However, some students take both. Data was collected from 60 students who took both college entrance exams. The average SAT score was 912 with a standard deviation of 180. The average ACT score was 21 with a standard deviation of 5. The correlation between the two variables equals 0.817. 1. To predict the SAT score from a student's ACT score, what is the equation of the least- squares regression line? (1) y ˆ = 0.3027 + 0.0227 x (2) y ˆ = 294.348 + 29.412 x (3) y ˆ = 156 + 36 x (4) Cannot be determined from the information given. 2. What fraction of the variation in the values of the SAT scores is accounted for by the linear relationship between SAT and ACT scores? (1) 66.7% (2) 81.7% (3) 90.4% (4) Cannot be determined from the information given.

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Page 2 3. Recall that when we standardize the values of a variable, the standardized value has mean 0 and standard deviation 1. Suppose we measure two variables X and Y on each of several subjects. We standardize both variables and compute the least-squares regression line of Y on X for these standardized values. Suppose the slope of this least- squares regression line is 0.44. What conclusion can we draw? (1) The intercept will be 1.0. (2) The intercept will also be 0.44. (3) The correlation will be 1.0. (4) The correlation will be 0.44. 4. Using least-squares regression, it is determined that the logarithm (base 10) of the population of a country is related to the year by the following equation: log(population) = 13.5 + 0.01×(year) Based on this equation, what will the (approximate) population of the country in the year 2006 be? (1) 6.56 (2) 706 (3) 2,006,000 (4) 3,630,780 Use the following to answer questions 5 -- 6: A researcher wishes to determine whether the rate of water flow (in liters per second) over an experimental soil bed can be used to predict the amount of soil washed away (in kilograms). The researcher measures the amount of soil washed away for various flow rates, and from these data calculates the least-squares regression line to be amount of eroded soil = 0.4 + 1.3 × (flow rate) 5. What do we know about the correlation between amount of eroded soil and flow rate?
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