A financial analyst is examining the relationship between stock prices and earnings per share. She chooses publicy 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--0.064 + 0.041x. This line, along with a scatter plot of her data, is shown below. Earnings per Current stock price, y (in dollars) 1.41 share, x (in dollars) 28.99 53.10 2.69 43.04 1.57 29.74 O80 24.87 1.10 17.31 58.56 2.16 32.99 1.52 21.47 0.80 38.90 1.36 42.65 1.13 49 83 1.71 13.50 0.48 Earnings per share, (in dollars) 40.86 1.69 58.19 2.72 37.87 1.16 Send data to caliculator v Send data to Ecel Based on the sample data and the regression line, complete the folowing. (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. e) According to the regression equation, for an increase of one dollar in earnings per share, there is a carresponding (Choose one) Vof 0.041 dolars in current stock price. e) From the regression equation, what is the predicted current stock price (in dollars) when the carnings per share is 42.65 dollars? (Round your answer to at least two decimal places.) (4) From the regression equation, what is the predicted current stock price (in dollars) when the earnings per share is 50.32 dollars? (Round your answer to at least two decimal places.) Current stock price, y (Sop u)

A financial analyst is examining the relationship between stock prices and earnings per share. She chooses publicy 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--0.064 + 0.041x. This line, along with a scatter plot of her data, is shown below. Earnings per Current stock price, y (in dollars) 1.41 share, x (in dollars) 28.99 53.10 2.69 43.04 1.57 29.74 O80 24.87 1.10 17.31 58.56 2.16 32.99 1.52 21.47 0.80 38.90 1.36 42.65 1.13 49 83 1.71 13.50 0.48 Earnings per share, (in dollars) 40.86 1.69 58.19 2.72 37.87 1.16 Send data to caliculator v Send data to Ecel Based on the sample data and the regression line, complete the folowing. (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. e) According to the regression equation, for an increase of one dollar in earnings per share, there is a carresponding (Choose one) Vof 0.041 dolars in current stock price. e) From the regression equation, what is the predicted current stock price (in dollars) when the carnings per share is 42.65 dollars? (Round your answer to at least two decimal places.) (4) From the regression equation, what is the predicted current stock price (in dollars) when the earnings per share is 50.32 dollars? (Round your answer to at least two decimal places.) Current stock price, y (Sop u)

Linear Algebra: A Modern Introduction

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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Question

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--0.064 + 0.041x. This line, along with a scatter plot of her data, is shown below.
Earnings per Current stock
price, y
(in dollars)
share, x
(in dollars)
28.99
1.41
53.10
2.69
43.04
1.57
29.74
0.80
24.87
1.10
17.31
0.88
58.56
2.16
32.99
1.52
21.47
0.80
38.90
1.36
42.65
1.13
49.83
1.71
13.50
0.48
Earnings per share, x
(in dollars)
40.86
1.69
58.19
2.72
37.87
1.16
Send data to calculator
Send data to Excel
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.
greater than
less than
(b) According to the regression equation, for an increase of one dollar in earnings per share, there is a corresponding
(Choose one) v of 0.041 dollars in current stock price.
(c) From the regression equation, what is the predicted current stock price (in dollars) when the earnings per share is 42.65
dollars? (Round your answer to at least two decimal places.)
(d) From the regression equation, what is the predicted current stock price (in dollars) when the earnings per share is 50.32
dollars? (Round your answer to at least two decimal places.)
Current stock price, y
(in dollars)

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An article included a summary of findings regarding the use of SAT I scores, SAT II scores, and high school grade point average (GPA) to predict first-year college GPA. The article states that "among these, SAT II scores are the best predictor, explaining 17 percent of the variance in first-year college grades. GPA was second at 15.2 percent, and SAT I was last at 13.1 percent." If the data from this study were used to fit a least squares line with y = first-year college GPA and x = high school GPA, what would the value of r2 have been? R2 ____________________%
A chemical company, seeking to study the effect of extraction time on the efficiency of an extraction operation, obtained the data from a table: Fit a straight line to the data given with the least squares method and use it to predict the extraction efficiency that would be expected when the extraction time is 35 minutes. x = Extraction time (minutes)y = Extraction efficiency (%)
How many indicator variables would be included in the model in order to prevent the least squares estimation from failing?

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