A regression model was constructed by regressing Y on 5 explanatory variables, X1, X2, X3, X4, and X5. There were n = 40 observations (rows) in the data set. In this case, the degrees of freedom (d.f.) for the error term in the model is:
Solution:
Given: A regression model was constructed by regressing Y on 5 explanatory variables, X1, X2, X3, X4, and X5.
thus k = Number of indepndent ( explanatory ) variables = 5
n = total observations = 45
We have to find the degrees of freedom (d.f.) for the error term in the model.
dferror = n - k - 1
dferror = 40 - 5 - 1
dferror = 34
Thus the degrees of freedom (d.f.) for the error term in the model is 34
A regression model was constructed by regressing Y on 5 explanatory variables, X1, X2, X3, X4,...
Additional Problem A researcher collected data on Y and four X-variables: X1, X2, X3, X4, and he wants to obtain a regression model. However, he is not sure if all the four X-variables should be included in the model. He provides you with the information shown below, namely, the SSR obtained when Y was regressed on each subset of X-variables. Also given: SST-100, and that the sample size is n 12. Your task Apply the Forward-Stepwise selection method, with a-to-enter-...
Consider a multiple regression model of the dependent variable y on independent variables x1, X2, X3, and x4: Using data with n 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: y0.35 0.58x1 + 0.45x2-0.25x3 - 0.10x4 He would like to conduct significance tests for a multiple regression relationship. He uses the F test to determine whether a significant relationship exists between the dependent variable and He uses the t...
4. Testing for significance Aa Aa Consider a multiple regression model of the dependent variable y on independent variables x1, x2, X3, and x4: Using data with n = 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: 0.04 + 0.28X1 + 0.84X2-0.06x3 + 0.14x4 y She would like to conduct significance tests for a multiple regression relationship. She uses the F test to determine whether a significant relationship exists...
Use the following linear regression equation to answer the questions. x1 = 1.5 + 3.4x2 – 8.3x3 + 2.3x4 (a) Which variable is the response variable? Which variables are the explanatory variables? (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant? x2 coefficient? x3 coefficient? x4 coefficient? (c) If x2 = 1, x3 = 8, and x4 = 6, what is the predicted value for x1? (Use 1 decimal place.) (d) Explain how...
Suppose we have 5 independent and identically distributed random variables X1, X2, X3, X4,X5 each with the moment generating function 212 Let the random variable Y be defined as Y = Σ We were unable to transcribe this image
Consider the multiple regression model shown next between the dependent variable Y and four independent variables X1, X2, X3, and X4, which result in the following function: Y = 33 + 8X1 – 6X2 + 16X3 + 18X4 For this multiple regression model, there were 35 observations: SSR= 1,400 and SSE = 600. Assume a 0.01 significance level. What is the predictions for Y if: X1 = 1, X2 = 2, X3 = 3, X4 = 0
4) Repair time of a car can be modeled by linear regression using months since the type of repair (X1), drive type (X2), servicing frequency (X3), and driving frequency (X4) as predictors. The model obtained was Y = 2.5 +1.7X1 – 3.5X2 + 6.2X3 – 4.7X4. The model was built based on 40 cars and the standard errors for X1, X2, X3, and X4 were 3.4, 2.6, 2.8, and 3.9 respectively. If the F-stat is 5.8, a) Find R2. b)...
Suppose we have 5 independent and identically distributed random variables X1, X2, X3, X4,X5 each with the moment generating function 212 Let the random variable Y be defined as Y = Σ Find the joint probability that all Xi, (i-1,.5), are larger than 9.
Suppose we have 5 independent and identically distributed random variables X1, X2, X3, X4,X5 each with the moment generating function 212 Let the random variable Y be defined as Y = Σ Find the probability that Y is larger than 9. Prove that the distribution you use is the exact distribution, nota Central Limit Theorem approximation
Run the following multivariate linear regression models:
Model 1: X3 and X4
Model 2: X2,X3,and X4Model 3: X1, X3 and
X4Discuss the correlation
between each two variables using adjusted R2 and P-value. Write the
estimated equation of Y for each regression model. Briefly comment
of the Residual Plots.
SUMMARY OUTPUT Regression Statistics Tourist arrivals (X3) Residual Plot Mu R Square Adjusted R Square Standard Error Observations 0.77706686 0.60383291 0.58622549 26011267.3 48 ANOVA Significance F 4.6406E 16 2.3203E 16 34.2942181 8.9591E-10...