3. Show manual computation. Refer to the table below. x2 y2 Statistics (x) Calculus (y) xy 30 28 22 32 27 30 27 33 29 30 27 28 27 32 27 32 22 25 28 32 21 25 21 30 28 32 20 26 29 30 a) What is the correlation coefficient? Interpret the result. b.) What is the best fit line that best describes the above data? c.) Using the regression line at (b), what would be the score of a student in calculus if the student got 19 in statistics?
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- The table below gives the number of hours seven randomly selected students spent studying and their corresponding midterm exam grades. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the midterm exam grade that a student will earn based on the number of hours spent studying. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Studying 1 1.5 2 2.5 3 3.5 4.5 Midterm Grades 61 62 75 77 79 83 88 Table Step 1 of 6 : Find the estimated slope, y intercept and correlation cofficient. Round your answer to three decimal places.The numbers of pass attempts and passing yards for seven professional quarterback for a recent year are listed in the table below. Round all answers to the nearest 1000th. Pass attempts (x) 449 565 528 197 670 351 218 Passing Yards (y) 3265 4018 3669 1141 5177 2362 1737 Calculate the sample correlation coefficient, r. Describe the type of correlation coefficient and interpret the correlation in the context of the data. Find the equation of the regression line for the data. Use the regression equation to predict the average number passing yards if the pass attempts are 250.The data below is 12 observations of Math SAT scores (x) and scores on Math placement test (y). Calculate the linear correlation coefficient, rr. Enter your answers to two decimal places. X Y 420 426 410 360 600 575 460 538 550 553 480 407 560 635 450 388 400 383 430 402 470 462 440 437 rr =
- The table below gives the age and bone density for 5 women. Use the equation of the regression line, y= b0 + b1x, for predicting a women's bone density based on her age. The correlation coefficient may or may not be statically significant for the data given. Remember it wouldn't be appropiate to use regression line to make a prediction if the correlation coefficient isn;t statically significant. (y has a "hat" on the top) age 39 51 54 56 67 bone density 355 349 347 315 313 Find the estimated slope. Rund your answer to three decimal places. Find the estimated y-intercept. Round your answer to three decimal places. Determine the value of the dependent variable y at x+ 0 (y has a "hat" onthe top) Find the estimated value of y when x = 51. Round your answer to three decimal places. Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the valueof the…9. Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below. Calories, x Sodium, y 160 130 330 120 70 190 (a) x = 170 calories (c) x = 150 calories 180 (b) x = 80 calories 420 470 360 250 530 (d) x = 210 calories Find the regression equation. x+( (Round to three decimal places as needed.) y = Choose the correct graph below. OA. О В. OC. OD. 560- 560 560 560- 200 G 0IN T> 200 200 Calories Calories Calories Calories (a) Predict the value of y for x = 170. Choose the correct answer below. O A. 411.632 O B. 543.752 O C. 455.672 O D. not meaningful (b) Predict the value of y for x = 80. Choose the correct answer below. O A. 411.632 О В. 257.492 O C.…c. 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 age and prices of 11 Nissan cars given in the following data: Age (in years) 5 4 6 5 5 5 6 6 2 7 7 Price (in $100s) 85 103 70 82 89 98 66 95 169 70 48 a. Obtain the correlation coefficient between the age and price of the cars. Interpret the value of the correlation coefficient. b. Obtain a regression equation of Price (dependent variable) on Age (Independent variable). c. What will be the Price of the car after 3 years? d. Find the coefficient of determination. Determine the percent of variation that is explained by the regression equation clearly.The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r= - 0.972. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y= - 0.0070x + 44.4405. Complete parts (a) and (b) below. Click the icon to view the data table. ..... (a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon? The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is %. (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. % of the variance in is by the linear model. Data Table (Round to one decimal p Full data set gas mileage Miles per Weight (pounds), x Weight (pounds), x Miles per Gallon, y Car Car Gallon, y…Amount of fertilizer (x) in pounds for each plot: 12, 5, 15, 17, 20, 14: Bushels of tomatoes harvested (y) 24 22 31 33 21 28: Round all values to three decimal places. a) Find the equation of the regression line (line of best fit). b) Calculate the correlation coefficient (r). c) Determine if there is a significant linear correlation. d) If the linear relation is significant, predict how many bushels of tomatoes would be harvested if 22 pounds of fertilizer was used.
- 4. A runner was tested on a treadmill. During the test, his speed x (in km/h) and his heart rate y were measured. The results are shown in the table. y 122 132 145 161 178 190 x 8 10 12 14 16 18 (a) Test for the significance of regression using the analysis of variance with a = 0.05. Find the P-value for this test. Can you conclude that the model specifies a useful linear relationship between these two variables? (b) Estimate ². (c) Estimate the standard error of the slope and intercept in this model. (d) Test the hypothesis that the increase in the speed of 1 km/h results in the runner's heart rate average increase of 7 points at a = 0.05. Suppose that the alternative hypothesis is that the average increase of the runner's heart rate in this situation does not equal 7 points.The following table shows students’ number of absences, x, and the student’s final grade,, y.# of absences x 6 2 15 9 12 5 8 Final grade y 82 86 43 74 58 90 78a) Calculate r, the correlation coefficient ________________b) Find the equation of the regression line __________________________________c) If a student is absent 4 times,, what grade does your regression line predict?__________________The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, y = bo + bjx, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 0.5 1.5 2.5 3 4 4.5 6 Overall Grades 89 86 81 79 72 67 62 Table Copy Data Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.