2. Consider the multiple regression model with three independent variables, under theclassical linear model assumptions MLR.1 through MLR.6:y= Bo+ B1x1 + B2x2 + B3x3 + u.You would like to test the null hypothesis Ho: B1 - 3ẞ2 = 1.a. Let B1 and B2 denote the OLS estimators of B1 and B2. Find Var(B₁ - 3B2) interms of the variances of B₁ and B2 and the covariance between them. What is thestandard error of B₁ - 3B2 ?b. Write the t statistic for testing Ho: ẞ1-3ẞ2 = 1.c. Define B1-3ẞ2 and ₁ = B₁ - 3ẞ2. Write a regression equation involving Bo,1, B2 and B3 that allows you to directly obtain ₁ and its standard error.

Given:Consider the multiple linear regression models with three independent variables as given…

Answered: 2. Consider the multiple regression…

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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Q3. Which one is not describe the Ordinary Least Squares (OLS) assumptions? A) The regression model should not be non-linear in the parameters B) The regression model is not incorrectly specified C) The number of parameters must be greater than the number of observations. D) Given the value of X, the variance of error is the same for all observations.
4. Can the speed of a vehicle be predicted by the age of its driver? The speeds Y (in km/h) of a sample of ten vehicles are recorded, along with the ages X of their drivers. From the data, we calculate i = 48.2, j = 107.8, (z:-2)² = 3669.6, (4- û)° = 752.7. The least squares regression line is calculated to be ŷ = 133.198 – 0.527x. It is also determined that 57.5% of the variation in the speed of a vehicle can be accounted for by its regression on the age of the driver. (a) What is the value of the correlation between the age of a driver and the speed of a vehicle? (b) Provide an interpretation of the slope of the least squares regression line. (c) Calculate a 95% confidence interval for the parameter 31 in the simple linear regression model. (d) We would like to conduct a hypothesis test at the 5% level of significance to determine whether a linear relationship exists between the age of a driver and the speed of a vehicle. Could the confidence interval in (c) have been used to conduct…
To help schedule staffing and equipment needs, a large hospital uses a multiple regression model to predict its 'bed census' y , the number of beds occupied at the end of each day. Using hospital records from the most recent 27 days, a total of 3 independent variables are used to find the estimated regression model. Let β1 , β2 , and β3 denote the coefficients of the 3 variables in this model. A computer printout indicates that the total sum of squares (SST) associated with the model is 710.26 and the corresponding regression sum of squares (SSR) is 305.30 . Using a significance level of 0.05 , can you conclude that at least one of the independent variables in the model provides useful (i.e., statistically significant) information for predicting daily bed census? Perform a one-tailed test. The null hypothesis: H0: The alternative hypothesis: H1 : at least one of the independent variables is useful The type of test statistic: (Choose…
7) Use computer software to find the best multiple regression equation to explain the variation in the dependent variable, Y, in terms of the independent variables, X1, X2, X3. 7)_ х, X2 98.6 101.2 87.4 97.6 108.5 110.1 102.4 96.7 110.4 CORRELATION COEFFICIENTS 100.9 98.2 104.3 Y/ X1 = 0.850 Y/ X2 = 0.742 102.3 99.8 107.2 101.5 100.5 105.8 101.6 103.2 107.8 101.6 107.8 103.4 99.8 96.6 102.7 88.9 COEFFICIENT OF DETERMINATION 100.3 104.1 YI X1 = 0.723 Y/ X2 = 0.550 YI X1, X2 = 0.867 99.2 %3D 97.6 75.1 97.2 76.9 99.7 97.3 84.6 102.0 96.0 90.6 94.3 99.2 103.1 97.7 100.3 105.1 101.1 102.3 100.3 96.4 104.1 104.4 104.4 105.3 110.7 108.5 107.6 127.1 111.3 B) Ý = 58.9+0.612X1 A) Ý = 57.6+0.153X, +0.270X2 C) Ý = 52.6+0.462X2 %3D D) Ý = 48.0+0.398X, +0.228X2 %3D
The following estimated regression equation was developed for a model involving two independent variables. ý = 40.7 + 8.63x, + 2.71.x, After x 2 was dropped from the model, the least squares method was used to obtain an estimated regression equation involving only X 1 as an independent variable. ŷ = 42.0 + 9.01x a. In the two independent variable case, the coefficient x 1 represents the expected change in Select v corresponding to a one unit increase in Select v when Select v is held constant. In the single independent variable case, the coefficient x 1 represents the expected change in Select v corresponding to a one unit increase in Select v b. Could multicollinearity explain why the coefficient of x 1 differs in the two models? Assume that x1 and x2 are correlated. Select
Consider the following data for two variables, x and y. \ table[[x, 9, 32, 18, 15, 26], [y, 9, 19, 20, 16, 22]] (a) Develop an estimated regression equation for the data of the form hat(y) = b + b₁x. (Round bo to two decimal 1 0 places and b₁ to three decimal places.) hat 1 (y) = 8.65 +0.427x Comment on the adequacy of this equation for predicting y. (Use α = 0.05.) The high p- value and low coefficient of determination indicate that the equation is inadequate. The high p-value and high coefficient of determination indicate that the equation is adequate. The low p-value and low coefficient of determination indicate that the equation is inadequate. The low p-value and high coefficient of determination indicate that the equation is adequate. hat 2 (y) = 10.54 +2.618x-0.054x Comment on the adequacy of this equation for predicting y. (Use a =0.05.) The high p-value and low coefficient of determination indicate that the equation is inadequate. The high p-value and high coefficient of…
29) Two variables are measured on a random sample of n = 23. The sample data results ina sample correlation of 0.393. If you fit a simple regression model to the data, whatvalue would the coefficient of determination (or R-squared) take on?A) 0.627B) 0.393C) 0.154D) 0.000E) 0.296
Suppose we conduct a study on the time spent studying for an exam and exam scores. We survey students in introductory statistics and find the explanatory variable (time, in hours) ranges from 0 to 16 and exam scores (in points, out of 100 maximum) range from 5 to 100. The correlation between time spent studying and exam scores is 0.80. We fit a simple linear regression model to these data and get the following least squares line: score = 4 + 6*(time). You pick a random student from the course and observe that the number of hours she studied for the exam is 1 standard deviation above the mean time spent studying. How many standard deviations above or below the mean exam score would you expect her to score?
12) Use computer software to find the best multiple regression equation to explain the variation in the dependent variable, Y, in terms of the independent variables, X1, X2, X3. 9896 29.1 1 421 9680 42.3 2 653 10449 29.8 3 573 10811 26.0 4 CORRELATION COEFFICIENTS 546 10014 34.3 5 499 10293 22.7 6 %3D 60% 0.00 Y/ X2=0.280 Y/ X3 = 0.930 504 9413 24.2 7 %3D 611 9860 31.6 8 %3D 646 9782 25.6 9 789 12139 37.9 10 COEFFICIENTS OF DETERMINATION 773 12166 33.9 11 YI X1 = 0.259 Y/ X2 = 0.079 YI X3 = 0.864 Y/ X1, X3 = 0.880 YI X1, X2, X3 = 0.884 753 9976 37.4 12 %3D 852 10645 27.0 13 %3D 755 9738 31.5 14 %3D 815 9933 39.9 15 %3D 902 10132 25.3 16 986 11145 30.4 17 909 9775 32.7 18 945 9549 35.0 19 866 10077 33.8 20 1178 11550 29.4 21 1230 10600 37.1 22 1207 11280 42.9 23 968 12100 32.2 24 1118 12420 30.5 25 A) Î = 57.8+0.036X, +28.1X3 B) Ý = -21.1+0.36X, +2.62X, +27.6X3 %3D C) Ý = 201.7+0.40X, +22.3X3 D) Y = 308.6+ 29.9X3 %3D
In a study, data collected for 40 observations were used to model the dependent variable y with 8 independent variables under consideration, x1, x2, .. , Xg. Consider a stepwise regression run on the data. 1. What is the form of the model fit in step 1? How many models are fit? How is the "best" independent variable selected in this step? 2. What is the form of the model fit in step 2? How many models are fit? How is the "best" independent variable selected in this step? 3. What is the form of the model fit in step 3? How many models are fit? How is the "best" independent variable selected in this step? 4. The variables x3, x4, and x6 were deemed the best variables for predicting y. How do you recommend the researchers proceed from here? Why?
Q2. The Update to the Task Force Report on Blood Pressure Control in Children reported the observedaverage SBP in single years of age from age 1 to 17 based on prior studies. The data for boys of averageSBP at each age are given in HW 5 data.sav on Blackboard. Suppose we seek a more efficient way todisplay the data and choose linear regression to accomplish this task.1) Fit a regression line using age as independent variable and SBP as dependent variable. (Theappropriate output is required here if you used software)2) Interpret the regression equation.3) Provide and interpret a 90% confidence interval for the parameters of the regression line.4) Perform ANOVA test for the population slope. Use α = 0.05, and both rejection region and p-value to make a decision.5) What the predicted (estimated) blood pressure on average is for a 10-year-old boy as estimatedfrom the regression line?6) Interpret R2.7) Check the conditions for your regression analysis using the appropriate plots. Age…
The manufacturer of Beanie Baby dolls used quarterly price data for 2012/-2020/V (t = 1, ..., 36) and the regression equation Pt= a + bt+c₁D1 t + c2 D2 + + c3 D3 t to forecast doll prices in the year 2021. Pt is the quarterly price of dolls, and D1, D2t, and D3+ are dummy variables for quarters I, II, and III, respectively. DEPENDENT VARIABLE: PT R-SQUARE P-VALUE ON F 0.0001 OBSERVATIONS: F-RATIO 76.34 STANDARD 36 0.9078 PARAMETER VARIABLE ESTIMATE ERROR T-RATIOP-VALUE INTERCEPT 24.0 6.20 3.87 0.0005 T 0.8 0.240 3.33 0.0022 D1 -8.0 2.60 -3.08 0.0043 D2 -6.0 1.80 -3.33 0.0022 D3 -4.0 0.60 -6.67 0.0001 The estimated quarterly increase in price is and the estimated annual increase in price is Multiple Choice O O $1.50; $6.00 $1.40; $4.00 $0.60; $2.40 $0.80; $3.20 None of the choices are correct.

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