I need someone to check a statistic test can anyone help me.
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
1. To check if a linear model is the best fit for a dataset, we need to analyze the scatterplot and the residual plot. If the scatterplot shows a strong curve pattern or if the residual plot shows a curve pattern, it indicates that a linear model is not the best fit.
2. To find the correlation coefficient, we need to calculate the correlation between the x values (L1) and the y values. The correct answer is given as 0.9807.
3. The coefficient of determination indicates the percentage of variation in the dependent variable (y) that is explained by the least squares regression line (LSRL). To find it, we square the correlation coefficient. In this case, the answer is given as 96%.
4. To determine whether a linear model is the best fit for a dataset, we need to consider the scatterplot, the residual plot, and the coefficient of determination. Looking at the given dataset and its analyses, we can conclude that a linear model is not the best fit because both the scatterplot and the residual plot show a curve pattern.
5. The scatterplot of the fish population data shows a curve that represents exponential growth.
6. To find the new value of y when x=5 after completing an exponential transformation, we need to substitute the value of x into the transformed equation. The correct answer is given as 3.6756.
7. To find the linear transformation model, the correct equation is given as log y hat = 0.9013x + 0.6935.
8. To predict the number of fish in 12 months using the linear transformation model, we need to substitute x=12 into the equation. However, the equation for the linear transformation model is not provided, so we cannot provide an answer for this question.
9. To determine the residual for the observed data x=7 and y=70, we need to substitute the values of x and y into the power model equation and calculate the residual. The correct answer is given as 1.37.
10. The data represents a total of 445 people.
11. To find the marginal frequency distribution regarding effectiveness, we need to divide the count of people who found the calcium supplement effective by the total count. The correct answer is 249/445.
12. To find the marginal frequency distribution regarding calcium supplement, we need to divide the count of people who took a particular dosage of calcium supplement by the total count. The correct answer is 219/445 for the 500 mg calcium supplement and 226/445 for the 1,200 mg calcium supplement.
13. To find the percentage of people who found the calcium supplement effective in reducing blood pressure, we need to divide the count of people who found it effective by the total count and multiply by 100%. The correct answer is given as 55.95%.
14. To find the percentage of people who found the calcium supplement not effective in reducing blood pressure, we need to divide the count of people who found it not effective by the total count and multiply by 100%. The correct answer is given as 44.05%.
15. Based on the data, we can conclude that more calcium intake improves the probability of effectiveness in reducing blood pressure.
16. Possible lurking variables refer to additional factors that may influence the relationship between the variables being studied. In this case, the question states that there are no lurking variables.