Question 2 Use the table of measurements of length and force that you have been supplied with to complete the following activities: (a) Draw a scatter graph for your given data. Describe what the scatter graph is indicating. (b) Use the scatter graph to estimate the length for a force of 57N
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- Zipfs Law The following table shows U.S cities by rank in terms of population and population in thousands. City Rank r Population N New York 1 8491 Chicago 3 2722 Philadelphia 5 1560 Dallas 9 1280 Austin 11 913 San Francisco 13 852 Columbus 15 836 A rule known as Zipfs law tells us that it is reasonable to approximate these data with a power function. a Use power regression to express the population as a function of the rank. b Plot the data along with the power function from part a. c Phoenix is the sixth largest city in the United States. Use your answer from part a to estimate population of Phoenix. Round your answer in thousands to the nearest whole number. Note: The actual population is 1537 thousand.The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.2. Use the table of measurements of length and force that you have been supplied with to complete the following activities: (a) Draw a scatter graph for your given data. Describe what the scatter graph is indicating. (b) Use the scatter graph to estimate the length for a force of 57N (c) Calculate the line of regression of extension on force (Y on X) (d) Calculate the correlation coefficient (e) Explain what the correlation coefficient indicates (f) Use the equation for the line of regression to predict the length for a force of 57N (g) Compare the calculated value with the value that you have determined from the scatter graph. Force (N) 0 20 40 60 80 Length (mm) 8 100 215 310 400.
- QUESTION 5 A student (just like you) is researching car loans issued at a local bank. She gathered a sample of 200 to determine if there is a relationship between the loan amount, length of the loan, and interest rate. The regression results are in the table below. Which model is more suitable for prediction and what is the best fit reason? Variable Model 1 Model 2 Constant 114.325 110.54 0.000 0.000 Interest Rate 106.505 108.650 (0.000) (0.000) Loan Length 0.2074 0.3290 (0.000) (0.006) Interest × Loan NA −0.1430 (0.0005) Adjusted R2 0.2178 0.2089 Model 1 is the most suitable because of the higher adjusted R2 value. Model 2 is the most suitable because of the lower adjusted R2 value. Neither provide enough results data to predict the model or reasoning. Model 2 is the most suitable because of the p-value variance.question 3 part 2 (thats the equation for the problem) The following estimated regression equation based on 10 observations was presented. ŷ = 21.1270 + 0.5508x1 + 0.4940x2 Here, SST = 6,736.125, SSR = 6,218.375, sb1 = 0.0815, and sb2 = 0.0561.Question 2 The following regression output was obtained. The regression model is Test scores onstudent teacher ratio. When your research assistant cut and pasted the results for you, therewere several vital pieces of information missing. See output below: SUMMARYOUTPUTRegression StatisticsMultiple R 0.226362751R Square (a)Adjusted R Square 0.048970335Standard Error 18.5809675Observations 420ANOVA df SS MS FRegression 1 7794.110041 7794.110041 22.57511055Residual 418 144315.4836 345.2523531Total 419 (b) Coefficients Standard Error t Stat P-valueIntercept 698.9329523 9.467491444str -2.279808287…
- Question 2 The following regression output was obtained. The regression model is Test scores onstudent teacher ratio. When your research assistant cut and pasted the results for you, therewere several vital pieces of information missing. See output below: SUMMARYOUTPUTRegression StatisticsMultiple R 0.226362751R Square (a)Adjusted R Square 0.048970335Standard Error 18.5809675Observations 420ANOVA df SS MS FRegression 1 7794.110041 7794.110041 22.57511055Residual 418 144315.4836 345.2523531Total 419 (b) Coefficients Standard Error t Stat P-valueIntercept 698.9329523 9.467491444str -2.279808287…QUESTION 4 (LINEAR REGRESSION)Based on the image attached, shows the results of one data collection. A physiotherapist advises 12 of his patients, all of whom had the same knee surgery done, to regularly perform a set of exercises. He asks them to record how long they practise. He then summarizes the average time they practised (X, time in minutes) and how long it takes them to regain their full range of motion again (Y, time in minutes).a) Construct the linear regression equation using the least square method.b) Based on the obtained linear regression line, explain the relationship between the variables X and Y.c) Sketch the scatter plot graph and the linear regression line of the recorded results.QUESTION 4 (LINEAR REGRESSION)Based on the image attached, shows the results of one data collection. A physiotherapist advises 12 of his patients, all of whom had the same knee surgery done, to regularly perform a set of exercises. He asks them to record how long they practise. He then summarizes the average time they practised (X, time in minutes) and how long it takes them to regain their full range of motion again (Y, time in minutes).a) Construct the linear regression equation using the least square method.b) Based on the obtained linear regression line, explain the relationship between the variables X and Y.c) Sketch the scatter plot graph and the linear regression line of the recorded results.*Help me solve these questions. Thank you.
- Question 4 The following table displays the mathematics test scores for a random sample of college students, along with their final SY16C grades. Fit the regression line y = a+bx to the data and interpret the results. Use the regression equation to determine the SY16C grade for a college student who scored 60 on their achievement test. What would their SY16C grade be? Mathematics test (x) SY16C grades (y) 1 39 65 2 43 78 3 21 52 4 64 82 5 57 92 6 47 89 7 28 73 8 75 98 9 34 56The Tiliche Corp. analyst conducted 10 independent timing studies in the manual spray painting section of the finishing department. The product line under study revealed a direct relationship between spray painting time and product surface area. The following data were collected (ignore the qualification factor): (image) a) Find the linear model relating standard time (y) to surface area (x) using linear regression.(x) using linear regression.b) How much time would you allocate to spray painting a new part with a surface area of 250 in2?surface area of 250 in2?c) Obtain the fitted value of y and the corresponding residual for a particular assembly (study #3), with a surface area of 250 inches2?(study #3), with an area of 150 square inches.d) Perform a significance test of the regression using α= 0.05. Find the P-value for this test.What are your conclusions?e) Estimate the standard errors of the slope and the value of the intercept.f) Calculate the coefficient of determination R2 .g)…Need help on part D! How does lateral acceleration—side forces experienced in turns that are largely under driver control—affect nausea as perceived by bus passengers? An article reported data on x = motion sickness dose (calculated in accordance with a British standard for evaluating similar motion at sea) and y = reported nausea (%). Relevant summary quantities are n = 17, xi = 223.9 , yi = 196 , xi2 = 3056.65 , xiyi = 2759.6 , yi2 = 2976 . Values of dose in the sample ranged from 6.0 to 17.6. (a) Assuming that the simple linear regression model is valid for relating these two variables (this is supported by the raw data), calculate and interpret an estimate of the slope parameter that conveys information about the precision and reliability of estimation. (Calculate a 95% CI. Round your answers to three decimal places.) , (b) Does it appear that there is a…