Problem 3 (15 points) (Core Course Outcomes 1,4 & 12)For problem 2 reporting results with at least 5 significant digits,a) calculate and report (=print) the order of accuracy p using linear least squares regression for the entire range of hk values wheretruncation errors dominate. Give (=print) the range of k values used for the fit, i.e., the minimum and maximum k values usedfor the fit.b) calculate and report (=print) the order of accuracy p using linear least squares regression for the entire range of hk values whereround-off errors dominates. Give (=print) the range of k values used for the fit, i.e., the minimum and maximum k values usedfor the fit.You do not have to determine the ranges of k values for a) and b) automatically in code, but can determine them from the graph ofproblem 2 and then set them in your script.Required submission:well commented script source code included in your Gradescope submission;printout of requested results in your Gradescope submission;

Problem Breakdown:You have to estimate the order of accuracy p using two different subintervals of…

Answered: Problem 3 (15 points) (Core Course…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
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?
Cellular Phone Subscribers The table shows the numbers of cellular phone subscribers y in millions in the United States from 2008 through 2013. Source: CTIA- The Wireless Association Year200820092010201120122013Number,y270286296316326336 (a) Find the least squares regression line for the data. Let x represent the year, with x=8 corresponding to 2008. (b) Use the linear regression capabilities of a graphing utility to find a linear model for the data. How does this model compare with the model obtained in part a? (c) Use the linear model to create a table of estimated values for y. Compare the estimated values with the actual data.
The data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) to (c) below. Click the icon to view the data table. (a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for females. Find the least-squares regression line for males. Data for licensed drivers by age and gender. y = x+ (Round the slope to three decimal places and round the constant to the nearest integer as needed.) Find the least-squares regression line for females. y =x+ Number of Number of (Round the slope to three decimal places and round the constant to the nearest integer as needed.) Number of Male Fatal Number of Female Fatal Licensed Drivers Crashes Licensed Drivers Crashes (b) Interpret the slope of the least-squares regression line for each gender, if…
Find the equation of the least squares regression line for the given data. (a) The number of crimes reported (in millions) and the number of arrests reported (in millions) by the U.S. Department of Justice for 14 years (b) Listed below are amounts of court fine revenue and salaries paid to the town justices. All amounts are in thousands of dollars, and all of the towns are in Dutchess County, New York.
An advertising firm wishes to demonstrate to potential clients the effectiveness of the advertising campaigns it has conducted. The firm is presenting data from 8 recent campaigns, with the data indicating an increase in sales for an increase in the amount of money spent on advertising. In particular, the least-squares Español regression equation relating the two variables cost of advertising campaign (denoted by x and written in millions of dollars) and resulting percentage increase in sales (denoted by y) for the 8 campaigns is y=6.70+0.19x, and the standard error of the slope of this least-squares regression line is approximately 0.13. Using this information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population slope B,. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.05 level of significance, and perform a two-tailed…
Please read the question carefully and show all your work. Use the formulas provided in the image.
Suppose the manager of a gas station monitors how many bags of ice he sells daily along with recording the highest temperature each day during the summer. The data are plotted with temperature, in degrees Fahrenheit (F), as the explanatory variable and the number of ice bags sold that day as the response variable. The least squares regression (LSR) line for the data is Bags = -151.05 +2.65Temp. On one of the observed days, the temperature was 82 °F and 68 bags of ice were sold. Determine the number of bags of ice predicted to be sold by the LSR line, Bags, when the temperature is (82\ \text (°F. J\\) Enter your answer as a whole number, rounding if necessary. Bags = 1.11 residual Incorrect Using the predicted value you just found, compute the residual at this temperature. 1.11 Incorrect ice bags ice bags
For major league baseball teams, do higher player payrolls mean more gate money? Here are data for each of the National League teams in the year 2002 . The variable x denotes the player payroll (in millions of dollars) for the year 2002 , and the variable y denotes the mean attendance (in thousands of fans) for the 81 home games that year. The data are plotted in Figure 1 scatter plot, as is the least-squares regression line. The equation for this line is =y+5.910.34x . Answer the following: 1. Fill in the blank: For these data, mean attendance values that are less than the mean of the mean attendance values tend to be paired with player payroll values that are _____ the mean of the player payroll values. Choose onegreater thanless than 2. Fill in the blank: According to the regression equation, for an increase of one million dollars in player payroll, there is a corresponding _____ of 0.34 thousand fans in mean attendance. Choose…
An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) through (d) below. (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. y=nothingx+(nothing) (Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.) (b) Interpret the slope and y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice. (Use the answer from part a to find this answer.) A. A weightless car will get nothing miles per gallon, on average. It is not appropriate to interpret the slope. B. For every pound added to the weight of the car, gas mileage in the city will decrease by nothing mile(s) per gallon, on…
Please show a step-by-step solution. Please explain your steps. Do not skip steps.
An article gave a scatter plot, along with the least squares line, of x = rainfall volume (m³) and y data on rainfall and runoff volume (n = runoff volume (m³) for a particular location. The simple linear regression model provides a very good fit to 15) given below. The equation of the least squares line is y = -2.364 + 0.84267x, ² 0.976, and s = 5.21. = x 5 12 14 17 23 30 40 47 55 67 72 81 96 112 127 y 3 9 12 14 14 24 27 45 38 46 52 71 81 100 101 (a) Use the fact that s = 1.43 when rainfall volume is 40 m³ to predict runoff in a way that conveys information about reliability and precision. (Calculate a 95% PI. Round your answers to two decimal places.) Ŷ 28.25 1x ) m³ Does the resulting interval suggest that precise information about the value of runoff for this future observation is available? Explain your reasoning. OYes, precise information is available because the resulting interval is very wide. 34.46 Yes, precise information is available because the resulting interval is very…

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