Calculate the correlation coefficient for the following data sets and then plot these data sets as scatter plots: (a) x 26 12 26 16 11 21 26 14 y 22 34 23 27 33 33 28 36 answer: r = -0.77357 (b) 9 10 17 28 5 u 3 8 v 30 30 48 38 38 40 49 43 7 answer: r = 0.53995
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- Use a computer or statistical calculator to calculate the correlation coefficient in parts a through c below. Cost Miles a. The table shows the approximate distance between selected cities and the approximate cost of flights between those cities. Calculate the correlation coefficient between cost and miles. 190 958 413 3095 r= (Round to three decimal places as needed.) 256 1998 90 429 436 3008 b. This table shows the same information, except that the distance was converted to kilometers by multiplying the numbers of miles by 1.609 and rounding to the nearest kilometer. What happens to the correlation coefficient when numbers are multiplied by a positive constant? Cost Kilometers O 190 1541 413 4980 (Round to three decimal places as needed.) 256 3215 90 690 436 4840 A. The correlation is The correlation coefficient remains the same when the numbers are multiplied by a positive constant. B. The correlation is The correlation coefficient increases when the numbers are multiplied by a…Listed below are annual data for various years. The data are weights (metric tons) of imported lemons and car crash fatality rates per 100,000 population. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using a =0.05. Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rates? Do the results suggest that imported lemons cause car fatalities? 228 Lemon Imports Crash Fatality Rate 266 358 484 531 15.8 15.7 15.5 15.2 14.8 O C. Ho: p=0 YD. Ho: p=0 H,:p>0 H1: p#0 Construct a scatterplot. Choose the correct graph below. O A. В. Oc. C. OD. Ay 17- Ay 174 Ay 17- Ay 17- 16- 16- 16- 16- 15- 15- 15- 15- 14- 14- 14+ 14- -> 600 -> 200 400 600 200 400 600 200 400 200 400 600 The linear correlation coefficient is r= -0.971. (Round to three decimal places as needed.) The test statistic is t= - 7.036 . (Round to three decimal places as needed.) The P-value is (Round to three decimal…The data below is 12 observations of Math SAT scores (x) and scores on Math placement test (y). Calculate the linear correlation coefficient, r. Enter your answers to two decimal places. Y 580 619 510 476 590 506 550 469 450 523 470 392 500 508 440 462 600 625 530 569 410 346 430 508 Question Help: Message instructor Submit Question Chp Ce %23 7 8. 9. W <6 64
- For a data set of chest sizes (distance around chest in inches) and weights (pounds) of eight anesthetized bears that were measured, the linear correlation coefficient is r = 0.996. Use the table available below to find the critical values of Ⓡ r. Number of Pairs of Data n 4 5 6 7 8 9 10 11 12 OA.-0.707 OB. +0.707 OC.-0.707, +0.707 OD. +0.754 Critical Value of r 0.950 0.878 0.811 0.754 0.707 0.666 0.632 0.602 0.576Listed below are annual data for various years. The data are weights (metric tons) of imported lemons and car crash fatality rates per 100,000 population. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using a = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rates? Do the results suggest that imported lemons cause car fatalities? 484 534 Lemon Imports Crash Fatality Rate 229 15.8 266 15.7 359 15.5 15.3 14.8 What are the null and alternative hypotheses? OA. H₂: p=0 H₁: p0 OD. Ho: p*0 H₁: p=0 OC. Ay 17+ 16- ܕ 15 14+ HHHH ▬▬▬▬▬ % do 6 200 400 600 G O D. Aу 17- 16 :|||||||* 15- 14+ 0 H °. C M o do 200 400 600 Q C sufficient evidence to support the claim that there is a linear correlation between lemon imports and crash fatality rates for a significance level of a = 0.05.The following table shows the weekly sales, test scores & achievement ratings of 5 salespersons working for a local car dealership: Salesperson Weekly Sales (Y) Sales Aptitude Test Score (x1) Mechanical Achievement (x2) Walters 11 10 6 Sullivan 5 4 2 Obmer 8 1 4 Smith 12 7 5 Jones 4 3 1 Brown 6 5 3 Black 7 2 2 Calculate the multiple correlation coefficient.. Select one: a. 0.925 b. 0.952 c. 0.295 d. 0.592
- The table below lists the mean systolic blood pressure during surgery (mmHg) along with blood loss (ml). Use this table to answer the next three (3) questions . BP Blood Loss 95274 90 170 Strength of Relationship 125 352 105317 weak moderate 110 171 105 150 90 245 90 120 none none 1/4 * 1/2; 3/4 13. Does the correlation coefficient indicate a strong linear correlation ? ( A) Yes ( B) No 14. Approximately what blood loss would you predict for a blood pressure reading of 140 ( A) 319 (B) 363 ( C) 401 ( D) 635 15. Do these data provide sufficient evidence , at the 0.05 level of significance , to indicate that the two variables are indeed correlated ?Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars). Determine if there is a significant linear correlation between advertising cost and profit . Use a significance level of 0.05 and round all values to 4 decimal places. Advertising Cost Profit 3 19 4 16 24 6 29 7 25 27 10 30 Ho: p = 0 На: р * 0 Find the Linear Correlation Coefficient r = Find the p-value p-value = The p-value is O Less than (or equal to) a O Greater than a The p-value leads to a decision to O Do Not Reject Ho O Accept Ho O Reject Ho The conclusion is O There is a significant negative linear correlation between advertising expense and profit. O There is a significant linear correlation between advertising expense and profit. O There is a significant positive linear correlation between advertising expense and profit. O There is insufficient evidence to make a conclusion about the linear correlation between advertising expense and…The data obtained in a study on the number of absences in virtual class and the final grades of seven randomly selected students from a mathematics class. The data are shown below. To determine the significance of the correlation coefficient at 0.05 level of significance, what is the calculated or computed value (CV)? Number of absences x Final in a virtual class grade y 82 6 86 15 43 9. 74 58 5 90 78 a. -1.59 b. 2.32 C. -2.32 d. 1.59
- A local store kept track of the number of advertisements it placed in local newspapers and the number of stereo systems it sold each week. Week 1 2 3 4 5 6 7 8 Advertisements, x 7 5 4 2 8 5 5 3 Stereos Sold, y 23 15 12 8 2 7 9 6 a) Create a scatter plot for the data showing Advertisements Vs. Stereos Sold. b) Determine the value of r, the correlation coefficient for the set of data and classify the type of correlation. c) What does this correlation coefficient suggest about the effectiveness of the advertisements? Explainc. Which of the following is the correct graph of the given data? -ОА. 10 1012 12 10 O C. 12- 81012 1012 Using the graph, explain the dramatic difference between the answers to parts (a) and (b). Choose the correct answer below. OA. The point (10,10) is not an outier, but it does have a strong effect on the least squares line and the correlation coefficient. OB. The point (10,10) does not have any effect on the least squares line and the correlation coefficient. OC. The point (10,10) is an outler that has a weak effect on the least squares line and the correlation coefficient. OD. The point (10,10) is an outlier that has a strong effect on the least squares line and the correlation coefficient.The accompanying table shows the ages (in years) of 11 children and the numbers of words in their vocabulary. Complete parts (a) through (d) below. Age, x Vocabulary size, y 1 5 2 240 3 560 4 1200 5 1900 6 2600 3 540 5 2200 2 280 4 1300 6 2300 (a) Display the data in a scatter plot. (b) Calculate the sample correlation coefficient r. (c) Describe the type of correlation, if any, and interpret the correlation in the context of the data. (d) Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation coefficient. Let α=0.01.