Need asap.... 10. In a multiple regression model with 3 explanatory variables X2,X3, and X4, the joint significance of X2, X3, and X4 can be testedusing a t test with N- 3 degrees of treedom, where N is the samplesize. (True/False).O TrueO False

Given: multiple regression model with 3 explanatory variables x2, x3 and x4 used degree of freedom =…

Answered: 10. In a multiple regression model with…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...

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2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1
Suppose a doctor measures the height, x, and head circumference, y, of 8 children and obtains the data below. Thecorrelation coefficient is 0.944 and the least squares regression line is y = 0.199x + 11.982. Complete parts (a) and (b)below.Height, x27.5 25.5 26.25 25.25 27.5 26.25 26 27.25 27.25 27 27.25 ФHead Circumference, # 17.5 17.0 17.2 17.0 17.5 17.3 17.2 17.4 17.3 17.3 17.4(a) Compute the coefficient of determination, R?R?.% (Round to one decimal place as needed.)(b) Interpret the coefficient of determination and comment on the adequacy of the linear model.Approximately % of the variation inis explained by the least-squares regression model.According to the residual plot, the linear model appears to be (Round to one decimal place as needed.)
Suppose that in a certain chemical process the reaction time (in hours) is related to the temperature (°F) in the chamber in which the reaction takes place, according to the simple linear regression model where β0 = 5.23, β1 = -0.01, and σ = 0.09. If the temperature is 260°F, what is the probability that the reaction time is between 2.51 and 2.7 hours? Suppose five observations are made independently on reaction time, each one for a temperature of 260°F. What is the probability that all five times are between 2.51 and 2.7 hours? If two independently observed reaction times for temperatures are 1° apart, what is the probability that the time at the higher temperature exceeds the time at the lower temperature?
Consider a regression analysis with n = 47 and three potential independent variables. Suppose that one of the independent variables has a correlation of 0.95 with the dependent variable. Does this imply that this independent variable will have a very large Student’s t statistic in the regression analysis with all three predictor variables?
Suppose a doctor measures the height, x, and head circumference, y, of 11 children and obtains the data below. The correlation coefficient is 0.899 and the least squares regression line is y=0.185x+12.276. Complete parts (a) and (b) below. Height, x 27.75 25.75 26.75 25.75 28 26.5 25.75 26.75 27 27.25 27.25 Head Circumference, y 17.4 17.1 17.2 16.9 17.4 17.1 17.1 17.3 17.3 17.3 17.4 (a) Compute the coefficient of determination, R2. R2=nothing% (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. Approximately nothing% of the variation in ▼ height head circumference is explained by the least-squares regression model. (Round to one decimal place as needed.)
Consider the fitted values from a simple linear regression model with intercept: yˆ = 7 + 4x. Assume that the total number of observations is n = 20. In addition, the explained sum of squares is SSE = 10 and the residual sum of squares is SSR = 30. Under the classical Gauss-Markov assumptions, a) What is the value of the R2 ?
A dietitian wishes to see if a person’s cholesterol level will be changed if the diet is supplemented by a certain mineral. Four subjects were pre-tested, and they took the mineral supplement for a 6-week period. The results are shown in the table. Is there sufficient evidence to conclude that the population mean of cholesterol levels has been changed after six weeks at α=0.2α=0.2? Assume that the differences are from an approximately normally distributed population. Subject Cholestrol Level (mg/dl) Cholestrol Level after 6 Weeks (mg/dl) dd ¯dd¯ (d−¯d)2(d-d¯)2 1 206 217 11 2 219 184 -35 3 202 204 2 4 213 205 -8 Total -30 a) Calculate the mean, the sum of the squared deviation from the mean, and the standard deviation of differences. Do not include the unit for each answer: ¯d=d¯= (do not round) ∑(d−¯d)2=∑(d-d¯)2= (do not round) sd=sd= (rounded to one decimal place) b) Perform the hypothesis test in the following steps: Step 1.…
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In a clinical study, a random sample of 540 participants agree to have their blood drawn, which is to be examined for the presence of antibodies against a certain contagious disease. It is found in 22% of the blood samples, which experimenters hope to extrapolate to the general population. From this random sample, 10 participants' blood samples are selected at random. If X is the number of samples out of the 10 who have these antibodies, what can we say about X? A. The sample size is not large enough for us to approximate X using a normal distribution B.The expected value of X is 22 C. X can be approximated using a normal distribution in lieu of a binomial distribution D. X has a sampling distribution that is normal
Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =-0.03+2.10RM+eHD R-squared =0.7 RML =0.06+1.60RM+eML R-squared =0.6 σM =0.15 where M is S&P/TSX Comp Index and RX is the excess return of stock X. What is the covariance and the correlation coefficient between HD and ML? For portfolio P with investment proportion of 0.4 in HD and 0.6 in ML, calculate the systematic risk, non-systematic risk, and total risk of P.
In the simple linear regression model , the Gauss Markov ( classical ) assumptions guarantee that the OLS estimator of the unknown parameters is BLUE. Among those assumptions , in order to have consistency of the OLS estimator we need ( this is a question on the necessary condition ): Question 4Select one: a. we need that the errors are not correlated with each others and that they have zero mean b. we need that the errors are homoscedastic ( all have the same variance) c. we need that the residuals are not correlated with the explanatory variables and that the residuals have zero mean d. we need that the errors have zero mean and that they are not correlated with the regressors ( no endogeneity) e. we need that the errors are homoscedastic ( all have the same variance) and not correlated with each others ( no serial correlation)
1. Consider the following set of points: {(-2 , -1) , (1 , 1) , (3 , 2)}a) Find the least square regression line for the given data points.b) Plot the given points and the regression line in the same rectangular system of axes

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10. In a multiple regression model with 3 explanatory variables X2, X3, and X4, the joint significance of X2, X3, and X4 can be tested using a t test with N- 3 degrees of treedom, where N is the sample size. (True/False). O True O False