Linear Regression Use linear regression to find the equation for the linear function that best fits this data. Round both numbers to two decimal places. Write your final answer in a form of an equation y=mx+b X y 12 72 87 3 4 5 6 104 132 149 166
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- 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.Car Speed The table shows the time t (in seconds) required for a car to attain a speed of s miles per hour from a standing start. Two models for these data are given below. t1=40.757+0.556s15.817lnst2=1.2259+0.0023s2 (a) Use the regression feature of a graphing utility to find a linear model t3 and an exponential model t4 for the data. (b) Use the graphing utility to graph the data and each model in the same viewing window. (c) Create a table comparing the data with estimates obtained from each model. (d) Use the results of part (c) to find the sum of the absolute values of the differences between the data and the estimated values found using each model. Based on the four sums, which model do you think best fits the data? Explain.Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
- question 22 The table below show data that has been collected from different fields from various farms in a certain valley. The table contains the grams of Raspberries tested and the amount of their Vitamin C content in mg. Find a linear model that express Vitamin C content as a function of the weight of the Raspberries. grams Vitamin Ccontent in mg 50 9.5 55 12 60 13.9 65 16.3 70 18.1 75 20.3 80 23 A) Find the regression equation: y= ______x+________ Round your answers to 3 decimal places B) Answer the following questions using your un-rounded regression equation. If we test 110 grams of raspberries what is the expected Vitamin C content? __________mg (round to the nearest tenth)Question 9 Assume a regression analysis yields a regression line with the value Y=$120,000 + $0.58X, where Y equals plant labor costs and X equals dollars of production output. If the company plans to produce $2,400,000 of product during the upcoming month, it would project plant labor costs to be: a. $324,000 b. $120,000 c. $204,000 d. $2,400,000QUESTION 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 #9 Find the regression equation, letting the first variable be the predictor (x) variable. Using the listed lemon/crash data, where lemon imports are in metric tons and the fatality rates are per 100,000 people, find the best predicted crash fatality rate for a year in which there are 400metric tons of lemon imports. Is the prediction worthwhile? Lemon Imports 233 269 364 492 548 Crash Fatality Rate 15.9 15.7 15.4 15.4 15 Find the equation of the regression line. y= ___________+( __________ ) x (Round the y-intercept to three decimal places as needed. Round the slope to four decimal places as needed.) The best predicted crash fatality rate for a year in which there are 400 metric tons of lemon imports is _________fatalities per 100,000 population. (Round to one decimal place as needed.) Is the prediction worthwhile? A. Since all of the requirements for finding the equation of the regression line are…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 22 A researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and the least squares line is: ˆy=4−5xy^=4-5x where x is the number of years of schooling completed and y is the number of pregnancies. The slope of the regression line can be interpreted in the following way: When amount of schooling increases by one year, the number of pregnancies tends to increase by 4. When amount of schooling increases by one year, the number of pregnancies tends to increase by 5. When amount of schooling increases by one year, the number of pregnancies tends to decrease by 4. When amount of schooling increases by one year, the number of pregnancies tends to decrease by 5.Question 16 Regression analysis was applied between sales (in $1000s) and advertising (in $100s), and the following regression function was obtained. = 500 + 4x Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is _____. $505,000 $900 $40,500 $900,000Question 5 Yummy Lunch Restaurant needs to decide the most profitable location for their business expansion. Marketing manager plans to use a multiple regression model to achieve their target. His model considers yearly revenue as the dependent variable. He found that number of people within 2KM (People), Mean household income(income), no of competitors and price as explanatory variables of company yearly revenue. The following is the descriptive statistics and regression output from Excel. Revenue People Income Competitors Price Mean 343965.68 5970.26 41522.96 2.8 5.68 Standard Error 5307.89863 139.0845281 582.1376385 0.142857 0.051030203 Median 345166.5 6032 41339.5 3 5.75 Mode #N/A 5917 #N/A 3 6 Standard Deviation 37532.51115 983.47613 4116.334718 1.010153 0.360838027 Sample…
