26. Suppose the population model is:Y₁ = Bo +3₁X₁ +3₂X₁2 +6₂Suppose the researcher has a random sample from this population. Let , be the residual of a regressionof Y on X₁ and X₂. In other words it is the residual obtained by estimating the model given above.Let Y, be the predicted value of Y in this regression. Let & be the residual of a regression of X₁ onX₂ (with a constant). Prove that:(4) ΣΥΣΤ(b) Σ",86 = 32

a) To prove that where is the predicted value of Y in the regression of Y on X1 and X2, and is…

Answered: 26. Suppose the population model is:…

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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The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1^x, for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Age Bone Density35 35043 34053 33954 32155 310 Step 3 of 6 : Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.
The least-square regression line for the given data is y = 0.449x - 30.27. Determine the residual of a data point for which x = 90 and y=10, rounding to three decimal places. Temperature, x Number of absences, y OA. -0.14 OB. 20.14 C. 115.78 OD. 10.14 72 3 85 7 91 10 90 10 88 8 98 15 75 100 4 15 80- 5
29)
The following sample contains the scores of 6 students selected at random in Mathematics and English. Use the scores in English as the dependent variable Y. Mathematics score (X) 70 92 80 74 65 83 English score (Y) 74 84 63 87 78 90 ∑x=464, ∑y=476,∑x^2=36354,∑y^2=38254, ∑xy=36926. Estimate the regression parameters and also write the prediction equation.
Suppose we have fit a multiple linear regression with 8 explanatory variables and an intercept with 85 observations. We want to test the joint significance of the first 5 explanatory variables using an F test. Please fill in the blanks for the numerator and denominator degrees of freedom of the F statistic of the test: "The F statistic is F(
Suppose that I want to estimate the effect of x₁ on y. Consider the univariate regression line: how to calculate a and b₁ using OLS? y = a + b₁x₁
The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1^x, for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Age Bone Density35 35043 34053 33954 32155 310 Step 4 of 6 : Determine the value of the dependent variable yˆ at x=0.
Suppose we have a multiple regression model with 2 predictors and an intercept. (Without any interaction or higher order terms, we have only the 2 predictors in the model and the intercept.) We have only n= 6 observations (so it would be rather silly to fit this model to this data, but let's pretend it is reasonable). We find the values of the first 5 residuals are: 2.6, 2.3, 2.5, -1.5, -1.4 What is the value of MSRes for this multiple regression model?
This table reports the regression coefficients when the returns of the size-institutionalownership portfolio (columns 1 and 2) returns are regressed on three variables: a constant(column 3), the stock market returns (column 4), and the change of the value weighted discountof the closed end fund industry (column 6). Columns 5 and 7 report the corresponding t-statistics of the coefficient estimates. Note that a t-statistic with an absolute value above 1.96means the coefficient estimate is significantly different from 0 at the 1% level. Column 8reports the R square of the regressions. Column 9 reports the mean institutional ownership ofeach portfolio. The last column reports the F-statistics for a multivariate test of the null hypothesis that the coefficient on ΔVWD in the Low (L) ownership portfolio is equal to theHigh (H) ownership portfolio. Two-tailed p-values are in parentheses. 1. What is the main finding of this Table? 2. What is the explanation for…
4. Consider a multiple linear regression model with two independent variables with 12 values in each variable. The coefficient of determination is obtained as 0.58. Evaluate the adjusted coefficient of detemination. for f nding Tote1 Cam ltinle lincor
Suppose the following regression equation was generated from the sample data of 50 cities relating number of cigarette packs sold per 1000 residents in one week to tax in dollars on one pack of cigarettes and if smoking is allowed in bars: PACKS, 58803.462982-1005.438507TAX, +284.030008BARS, + BARS, 1 if city / allows smoking in bars and BARS,= 0 if city i does not allow smoking in bars. This equation has an R² value of 0.305162, and the coefficient of BARS, has a value of 0,088136. Which of the following conclusions is valid? Answer Keypad Keyboard Shortcuts m Tables O If there is no cigarette tax in a city that allows smoking in bars, the approximate number of cigarette packs sold per 1000 people is 58803. O According to the regression equation, cities that allow smoking in bars have lower cigarette sales than cities that do not allow smoking in bars. O More than half of the variation in cigarette sales is explained by cigarette taxes and whether or not a city allows smoking in bars.…
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