(a) Suppose you are given the following (x, y) data pairs.126y43n USE SALTFind the least-squares equation for these data (rounded to four digits after the decimal).ý = 1.90481.1429(b) Now suppose you are given these (x, y) data pairs.439y126Find the least-squares equation for these data (rounded to four digits after the decimal).ý = -1.92900.7442X X(c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair?YesO No(d) Solve your answer from part (a) for x (rounded to four digits after the decimal).X = -1.12g0.7742X YDo you get the least-squares equation of part (b) with the symbols x and y exchanged?O YesNo(e) In general, suppose we have the least-squares equation y = a + bx for a set of data pairs (x, y). If we solve this equation forx, will we necessarily get the least-squares equation for the set of data pairs (y, x), (with x and y exchanged)? Explain using parts(a) through (d).O In general, switching x and y values produces the same least-squares equation.In general, switching x and y values produces a different least-squares equation.Switching x and y values sometimes produces the same least-squares equation and sometimes it is different.

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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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A financial analyst is examining the relationship between stock prices and earnings per share. She chooses publicly traded companies at random and records for each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with x denoting the earnings per share from the previous year, and y denoting the current stock price (both in dollars). Based on these data, she computes the least-squares regression line to be =y+−0.2130.046x. This line, along with a scatter plot of her data, is shown below. Based on the sample data and the regression line, complete the following. (a)For these data, current stock prices that are less than the mean of the current stock prices tend to be paired with values for earnings per share that are ▼(Choose one) the mean of the values for earnings per share. (b)According to the regression equation, for an increase of one dollar in earnings per share, there is a…
A financial analyst is examining the relationship between stock prices and earnings per share. She chooses publicly traded companies at random and records for each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with x denoting the earnings per share from the previous year, and y denoting the current stock price (both in dollars). Based on these data, she computes the least-squares regression line to be =y+−0.2130.046x. This line, along with a scatter plot of her data, is shown below. )From the regression equation, what is the predicted current stock price (in dollars) when the earnings per share is 52.82 dollars? (Round your answer to at least two decimal places.)
Given the bivariate data : x y 0 -0.1 1 -3.3 2 -6.1 3 -9.6 4 -12.2 Find the least squares regression line for the data . Round constants to the nearest hundredth . Use the equation of the least squares line to predict the value of y when x=3.6 .
(a) Suppose you are given the following (x, y) data pairs. x 2 3 6 y 4 3 9 Find the least-squares equation for these data (rounded to four digits after the decimal).ŷ = + x(b) Now suppose you are given these (x, y) data pairs. x 4 3 9 y 2 3 6 Find the least-squares equation for these data (rounded to four digits after the decimal).ŷ = + x(c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair? YesNo (d) Solve your answer from part (a) for x (rounded to four digits after the decimal).x = + yDo you get the least-squares equation of part (b) with the symbols x and y exchanged? YesNo (e) In general, suppose we have the least-squares equation y = a + bx for a set of data pairs (x, y). If we solve this equation for x, will we necessarily get the least-squares equation for the set of data pairs (y, x), (with x and y exchanged)? Explain using parts (a) through (d). Switching x and y values sometimes…
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A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression equation of the least squares line is ŷ = 3 + 1x. EX= 24 EX = 124EY= 42EY = 338 EXY = 196MSE = 4 Using the sums of the squares given above, determine the 90 percent confidence interval for the mean value of monthly tire sales when the advertising expenditure is $5.000. distance value = .20238 a. (6.08, 9.92) b. (3.235, 6.765) c. (2.465, 6.853) d. (5.325, 7.675)
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(a) Find the equation of the least-squares line for the data. (Round all numerical values to two decimal places.) y= ?
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