2. Suppose you are to fit a linear model which is forced to have an intercept equalto 5, of the form given by:Y₁ = 5 + B₁X₁ + &; for i = 1,2,.., nwhere & has mean 0 and variance o² for any value of X.a) Derive the least squares estimator, ₁ of the slope ₁.b) Find E(₁) and o² (B₁).c) Derive the maximum likelihood estimator, ₁ of the slope ₁. Is it the same asthe least squares estimator?d) What is the estimator of the variance of the random error term?e) Prove whether or not it is still true that Σ₁ e₁ = 0.

The given linear model is,Regression forms a basic tool in statistical analysis. It is highly useful…

Answered: Suppose you are to fit a linear model…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Q12) If the slope of the regression equation y=b0+b1×x is equal to negative, then; 1. as x increases y decreases 2.. as x changes, y does not change 3.. Either a or b is correct 4.. as x decreases y increases
11) A simple linear regression model based on 20 observations. The F-stat for the model is 21.44 and the SSE is 1.41. The standard error for the coefficient of X is 0.2. a) Complete the ANOVA table. b) Find the t-stat of the co-efficient of X c) Find the co-efficient of X.
Complete Table 3 and find the values of A and B for the straight line that provides the best least-squares fit to the data Table 3 y xy 1 2 3 7 4 9 5 12 Ex = Ey = Σxy Ex² =
4. Our R² implies that lots of stuff, other than health, also affects doctor visits. One such thing is a person's insurance status. The data file includes a third variable that records whether the person had health insurance during 2019. Estimation a regression of the form y = Bo + B₁x1 + B₂x₂ where x₁ is the health status variable from above, but now x₂ records whether the person had insurance. a) Interpret the estimate of B₁ in words. b) Interpret the estimate of B₂ in words. c) Forecast a person's number of doctor visits in 2019 if he/she was in excellent health, but did not have insurance. d) Forecast a person's number of doctor visits in 2019 if he/she was in poor health, and did have insurance. e) The R² for this regression is
One of the standard curves used is harmonic decline model, that is: Q = bx/(1+ ax²) where Q is the rate of production and x is the time, b and a are the constants of the regression model. If we apply linear least squares fit for estimating b and a, what will be the value of the summation of squared errors.S Sr x, Months 11 16 18 22 90 75 65 Q, Barrels/Day 1 9 44 100 50 Sr= {(y- P(x)} 2 - (9,- #2) ²
Over the years Olympic racers have been getting fasterin most events, and the women’s singles 500-meter kayakrace is no exception. A scatterplot displaying the data foryears since 1948 (x) and time in seconds (y) suggests thata linear model is appropriate. The equation of the leastsquares regression line is, yn = 144.627 - 0.776x, andr2 = 0.932.a) Interpret the value of r2 in this context.b) Compute and interpret the value of r in context.c) The Olympics are held every 4 years. What changein the winning time does this model predict from oneOlympics to the next?d) The residual for the winning time in 1980 was-1.795 seconds. Find this gold medal time.
The table shows the numbers of new-vehicle sales (in thousands) in the United States for Company A and Company B for 10 years. The equation of the regression line is ModifyingAbove y with caret equals 0.993 x plus 1 comma 195.82y=0.993x+1,195.82. Complete parts (a) and (b) below. New-vehicle sales left parenthesis Company Upper A right parenthesis comma x(Company A), x 4 comma 1674,167 3 comma 8823,882 3 comma 5693,569 3 comma 4433,443 3 comma 2993,299 3 comma 1173,117 2 comma 8372,837 2 comma 4982,498 1 comma 9401,940 2 comma 0842,084 New-vehicle sales left parenthesis Company Upper B right parenthesis comma y(Company B), y 4 comma 9204,920 4 comma 8444,844 4 comma 8374,837 4 comma 7104,710 4 comma 6754,675 4 comma 4284,428 4 comma 6604,660 3 comma 8323,832 2 comma 9272,927 2 comma 7532,753 Question content area bottom Part 1 (a) Find the coefficient of determination and interpret the result.…
If the slope of a regression line (b1) is 1.5, then a) for every unit of change in x, there is a change of 1.5 units in y b) for every unit of change in y, there is a change of 1.5 in x. c) the score of each case is 1.5 times higher on yt han on x d)y causes X
Show calculations or explanation for each question. a) Which of the following techniques is used to predict the value of one variable on thebasis of other variables?a. Correlation analysisb. Coefficient of correlationc. Covarianced. Regression analysis b) In the least squares regression line, y^=3-2x the predicted value of y equals:a. 1.0 when x = −1.0b. 2.0 when x = 1.0c. 2.0 when x = −1.0d. 1.0 when x = 1.0 c) In the simple linear regression model, the y-intercept represents the:a. change in y per unit change in x.b. change in x per unit change in y.c. value of y when x = 0.d. value of x when y = 0.

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