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Unit 4 Test
Multiple Choice
1. Which choices listed below indicate that a linear model is not the best fit for a dataset? Choose all that apply.
(3 points)
• Scatterplot shows a strong linear pattern.
• Scatterplot shows a curve pattern. *
• Residual plot shows a curve pattern.*
• Residual plot shows no pattern.
• Correlation coefficient is close to 1 or –1.
• Coefficient of determination is close to 1 or –1.
• Unexplained variation is close to 1 or –1.*
Use the dataset below to answer questions 2–4 .
x y

20 399
18 323
5 26
13 170
2 3
15 220
2 5
2.
Find the correlation coefficient using L1 as the x values. (1 point)
• 0.9617
• 0.9807*
• 20.64
• –57.44
3. Find the coefficient of determination. What percent of the variation is explained by the LSRL?
(1 point)
• 4%
• 98%
• 2%
• 96%*
4. Use the dataset and its analyses to determine whether a linear model is the best fit. Explain your reasoning. (3 points)


Scientists are studying the population of a particular type of fish. The table below shows the data gathered over a five–month time period. Use the data to answer questions 5–9.

Number of months Number of fish
0 8
1 39
2 195
3 960
4 4,738
5 23,375


5. What does the scatterplot of the data show? (1 point)
• a strong positive linear relationship
• a strong negative linear relationship
• a curve that represents exponential growth *
• a curve that represents exponential decay
6. Complete an exponential transformation on the y-values. What is the new value of y when x = 5?
(1 point)
• 4.3688
• 3.6756 *
• 0.6990
• 3.3757
7. Find the linear transformation model. (1 point)
• logy hat=o.6935•logx+ 0.9013
• log y hat=0.9013x+0.6935*
• log y hat=0.6935x+ 0.9013
• log y hat=0.9013•logx+ 0.6935
8.
Use the linear transformation model to predict the number of fish in 12 months. (2 points)


9. A power model is shown below. Determine the residual for the observed data x = 7 and y = 70.

log y hat=1.6+0.3logx (1 point)
• 71.37
• 1.37*
• 1.85
• –1.37
A medical study was conducted to determine if taking calcium is effective in reducing blood pressure. The results are shown in the table below. Use this information to answer questions 10–16.

500 mg calcium 1,200mg calcium
Supplement daily supplement daily

Effective 82 167 249

non effective 137 59 196

total 219 226 445


10. How many people does the data represent?
(1 point) 445

11. Find the marginal frequency distributions regarding effectiveness. (2 points) 249/196

12. Find the marginal frequency distributions regarding calcium supplement. (2 points) 219/226

13. According to the data, what percent of people taking a calcium supplement found it effective in reducing blood pressure? (1 point)
55.95%
14. According to the data, what percent of people taking a calcium supplement found it not effective in reducing blood pressure? (1 point) 44.05%

15. What conclusions can be made regarding the association among the effectiveness of taking a calcium supplement and reducing blood pressure? (4 points More calcium improves the probability of effectiveness.

16.
Identify any possible lurking variables. (2 points)
no lurking

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