Please read the question carefully and show all your work. Use the formulas provided in the image. 1. The last snowstorm lasted 6 hours. Over that time, the amount of snowfall wasmeasure hourly, except for at the 5th hour when Mr. Pearce watched the 3rdperiod of the Leaf game.a) Perform a linear regression using the least-squares method to find theequation of the line of best fit.Time (Hours)Total Accumulation (cm)x2ху831041261618ΣxyUseful Formulasn(E xy) (Ex)(Ey)a =n(Ex2) (Ex)²b = ỹах

Given dataTime(Hours) Total accumulation (cm) 2 8 3…

Answered: 1. The last snowstorm lasted 6 hours.…

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 34EQ

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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?
2. A company that holds the DVD distribution rights to movies previously released only in theaters wants to estimate sales revenue of DVDs based on box office success. The box office gross (in Php millions) for each of 22 movies in the year that they were released and the DVD revenue (in Php millions) in the following year are shown below and stored in (pic) a. construct a scatter plot. b. assuming a linear relationship, use the least-squares method to determine the regression coefficients b0 and b1.
Two specimens of cold rolled steel sheet, which have differentcopper contents and annealing temperature are measured in hardness with the following results: First column = HardnessSecond column = Copper contentThird column = Annealing temperature a) Create a scatter plot to verify that it is reasonable to assume that the regression of Y on x is linear. b) Fit a straight line using the method of least squares. c) Fit an equation of the form (image 2), where x1 represents the copper content, x2 represents the annealing temperature, and y represents the hardness.
A “Cobb–Douglas” production function relates production (Q) to factorsof production, capital (K), labor (L), and raw materials (M), and an errorterm u using the equation Q = λKβ1Lβ2Mβ3eu, where λ, β1, β2, and β3 areproduction parameters. Suppose that you have data on production and thefactors of production from a random sample of firms with the same Cobb–Douglas production function. How would you use regression analysis toestimate the production parameters?
An experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. ∑ X = 30 ∑ X 2 = 104 ∑ Y = 40 ∑ Y 2 = 178 ∑ XY = 134 Using the simple linear regression model, find the estimated y-intercept and slope and write the equation of the least squares regression line.
The least-squares regression equation is y=761.7x+13,208 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7483. In a particular region, 26.5 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $30,074. Is this income higher than what you would expect? Why?

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