In the following problems, find the equation of the least squared regression line and the correlation coefficient. Then perform a hypothesis test to determine if there is a significant relationship between the two variables. Use the p-value method and show all 5 steps of the hypothesis test. Test at a= 0.05 2. A random sample of scoring leaders in the NHL showed the following numbers of assists and total points. Assists, x 26 29 32 34 36 37 40 Total Points, y 48 68 66 69 76 67 84
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In the following problems, find the equation of the least squared regression line and the
2. A random sample of scoring leaders in the NHL showed the following numbers of assists and total points.
| Assists, x | 26 | 29 | 32 | 34 | 36 | 37 | 40 |
| Total Points, y | 48 | 68 | 66 | 69 | 76 | 67 | 84 |
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- The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, Y=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Price in dollars 31 38 42 44 46 Number of Bids 3 4 6 7 9 Summation Table X Y XY X2 Y2 BID 1 31 3 93 961 9 BID 2 38 4 152 1444 16 BID 3 42 6 252 1764 36 BID 4 44 7 308 1936 49 BID 5 46 9 414 2116 81 SUM 201 29 1219 8221 191 Step 1: Find the estimated slope. Step 2: Find the estimated y-intercept. Step 3: Determine the value of the dependent variable Y at x=0. Step 4: Find the estimate value of y when x=42. Step 5: Substitute the values you found in steps 1 and 2 into the equation for the…In a dataset, X is the independent variable, and Y is the dependent variable. Which of the following statement is correct? None of these Regression between X and Y determines the nature of the relationship between the variables. Regression between X and Y determines whether there exists any relationship between the variables. Correlation between X and Y determines the nature of the relationship between the variables.o pis pe Suppose a doctor measures the height, x, and head circumference, y. of 11 children and obtains the data below. The correlation coefficient is 0.899 and the least squares regression line is y = 0.185x+ 12.276. Complete parts (a) and (b) below. Height, x Head Circumference, y 17.4 17.1 17.2 16.9 17.4 17.1 17.1 17.3 17.3 17.3 17.4 27.75 25.75 26.75 25.75 28 26.5 25.75 26.75 27 27.25 27.25 (a) Compute the coefficient of determination, R?. R2 = % (Round to one decimal place as needed) (b) Interpret the coefficient of determination k Approximately % of the variation in (Round to one decimal place as needed.) is explained by the least-squares regression model. Enter your answer in each of the answer boxes. Save for Later DUE RTTT:DY PIVT Score: o:5SYO Tor Tv attempts 3:35 PA- a 2/22/202 Type here to search insert prt sc 4+ backsp %23 6. 8.
- Research was conducted on the amount of training for 5K and the time a contestant took to run the race. The researcher recorded the number of miles during training ( a 1 month period) and the time to complete the 5K. The results are below. Miles Trained 45 77 37 25 60 64 Time (Minutes) 32.9 28 36.2 27.5 19.5 18.3 a) Give the correlation coefficient. r = b) Give the equation of the regression line. Round the values to 4 deimal places.This is in the form y = ax + b, so the slope goes in the first box and the y-inercept in the 2nd box.y = x + c) Interpret the y-intercept (Explain it's meaning, do not just give its value.)d) Predict the time in the 5K if someone trained 37 miles.Use the rounded values entered for the slope and intercept of the regression line to compute the predicted y-value.y = e) Give the residual for 37 miles trained.This is the actual y value for the runner who trained for miles minus the predicted value.Residual=ANSWER D ONLY9. 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.…
- Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with fish treats after each successful attempt at a new trick. The following table lists the dolphins, the number of treats per success given to each, and the average number of attempts necessary for each to learn to perform the tricks. Dolphin Number of Treats Number of Attempts Diana 2 Frederick 4 Fatima Marlin Ŷ = bX + a You can use the preceding sample data to obtain the regression line, where Ŷ is the predicted value of Y: b = One formula for the slope of the regression line is as follows: SP = To calculate the slope, first calculate SP and SSx: 1 3 and SSx = ∞587 (Hint: For SP use the computational formula and for SSx use the definitional formula.) The slope of the regression line is Frederick Fatima Marlin The difference between Y and Ŷ for a particular sample point (observation) is called a residual. Calculate the predicted Y (Y) for each of the dolphins, and then calculate the residuals. 4…Post secondary education information was examined for a random selection of states. The data below show the number of community colleges in the number of universities for each particular state. Community: 12, 17, 13, 10, 8 University: 4, 6, 5, 4, 3 A. Create a scatterplot of the given data sets B. Find the correlation coefficient of the sets of data. C. Create the equation of the regression line for the data and evaluate it when X=300.The coefficient of determination (r2) is a measure of the: a.) amount of variance in the dependent variable explained by the independent variable. b.) correlation between two variables. c.) variability of the dependent measure. d.) slope of a regression line.
- Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with fish treats after each successful attempt at a new trick. The following table lists the dolphins, the number of treats per success given to each, and the average number of attempts necessary for each to learn to perform the tricks. Dolphin Number of Treats Number of Attempts Diana 4 5 Frederick 2 8 Fatima 1 8 Marlin 3 7 You can use the preceding sample data to obtain the regression line, where Ŷ is the predicted value of Y: ŶŶ = = bX + abX + a One formula for the slope of the regression line is as follows: bb = = SPSSxSPSSx To calculate the slope, first calculate SP and SSxx: SP = __?__ , and SSxx = _?_ . (Hint: For SP use the computational formula and for SSxx use the definitional formula.) The slope of the regression line is , and the Y intercept of the regression line is ___?__ . The difference between Y and…The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. 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. Price in Dollars 102 137 139 171 186 Number of Bids 10 11 16 17 20 Table Step 6 of 6 : Find the value of the coefficient of determination. Round your answer to three decimal places.
