The following bivariate data represents a report about the x: time (in years) and y: the average height of a person can jump (in cm): [Hint: better if you start with expanding the table with multiple columns when you take the transpose of this one) X 10+E 20+F 30+G 40+H 50+I y 20 60 80 70 60 a) Find the least squares estimate of the regression line with assuming that the simple linear regression is valid. (Find the regression equation). b) Estimate an average jump height when the person's age becomes 35 based on your regression model with 95% confidence interval.

The following bivariate data represents a report about the x: time (in years) and y: the average height of a person can jump (in cm): [Hint: better if you start with expanding the table with multiple columns when you take the transpose of this one) X 10+E 20+F 30+G 40+H 50+I y 20 60 80 70 60 a) Find the least squares estimate of the regression line with assuming that the simple linear regression is valid. (Find the regression equation). b) Estimate an average jump height when the person's age becomes 35 based on your regression model with 95% confidence interval.

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 29EQ

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Hello there! Can you help me solve a problem with two subparts? Thank you! Question: If a machine learns the least-squares line that best fits the data shown below, what will the machine pick for the value of y when x= 2? How closely does this match the data pt at x = 2 fed into the machine? (0, 2), (1, 2), (2, 5), (3, 5) First subpart When x = 2, the machine will pick a value of __ for y. Second subpart Three options: (a) This is __ away from the y-value fed into the machine for x= 2, which is too large to be expected for the best fit line. (b) This is exactly the same as the data point fed into the machine. (c) This is __ away from the y-value fed into the machine for x= 2, which is reasonably close considering the range of y-values in the data set.
Consider the following model y = β0 + β1x + ∈, where y is the daily rate of return of a stock, and x is the daily rate of return of the stock market as a whole, measured by the daily rate of return of Standard & Poor's (S&P) 500 Composite Index. Using a random sample of n = 12 days from 2007, the least squares lines shown in the table below were obtained for four firms. The estimated standard error of 1 is shown to the right of each least squares prediction equation. Estimated Market Model & Estimated Std Error of β1 Company A y = .0010 + 1.40x, β1 = .03Company B y = .0005 - 1.21x, β1 = .06Company C y = .0010 + 1.62x 1.34, β1 = 1.34Company D y = .0013 + .76x .15, β1 = 0.15 Calculate the test statistic for determining whether the market model is useful for predicting daily rate of return of Company A's stock. a) 161.6b) 1.40 ± .067 c) 1.40d) 46.7
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