True or False:
1. The fit of the regression equations yˆ = b0 + b1x + b2x2 and yˆ = b0 + b1x + b2x2 + b3x3 can be compared using the coefficient of determination R2.
2. The fit of the models y = β0 + β1x + ε and y = β0 + β1ln(x) + ε can be compared using the coefficient of determination R2.
3. A quadratic regression model is a special type of a polynomial regression model.
1. False. The coefficient of determination of the two models cannot be compared because the number of independent variables in the model are different. In the first equation, the number of independent variables are two while in the second equation, the number of independent variables are three. Thus, R squared value of the two equations cannot be compared.
2. True. The fit of the model can be compared in this case because the number of independent variables in the equation in the above case are same. The fit will tell whether logarithmic transformation of the independent variable is a better fit as compared to the no transformation of the independent variable. Thus, the two can be compared in this case.
3. True. The statement is true because a quadratic regression model is a special type of a polynomial regression model. Polynomial model includes quadratic regression model in it.
True or False: 1. The fit of the regression equations yˆ = b0 + b1x + b2x2 and yˆ = b0 + b1x + b2x2 + b3x3 can be compared using the coefficient of determination R2. 2. The fit of the models y = β0 +...
True or False: 1. The fit of the regression equations yˆ = b0 + b1x + b2x2 and yˆ = b0 + b1x + b2x2 + b3x3 can be compared using the coefficient of determination R2. 2. The fit of the models y = β0 + β1x + ε and y = β0 + β1ln(x) + ε can be compared using the coefficient of determination R2. 3. A quadratic regression model is a special type of a polynomial regression model.
2) Suppose the regression model y = B0 + B1x1 + B2x2 + B3x3 + B4x1x2 + B5x1x3 + B6x2x3 was fit to n = 27 data points with SSE = 2000.0. a) Set up the null and alternative hypotheses for testing whether the interaction terms are significant. b) Give the reduced model necessary to test the significance of the interaction terms. c) The reduced model resulted in SSE = 2800. Calculate the value of the test statistic appropriate for...
2) Suppose the regression model y = B0 + B1x1 + B2x2 + B3x3 + B4x1x2 + B5x1x3 + B6x2x3 was fit to n = 27 data points with SSE = 2000.0. a) Set up the null and alternative hypotheses for testing whether the interaction terms are significant. b) Give the reduced model necessary to test the significance of the interaction terms. c) The reduced model resulted in SSE = 2800. Calculate the value of the test statistic appropriate for...
(Do this problem without using R) Consider the simple linear regression model y =β0 + β1x + ε, where the errors are independent and normally distributed, with mean zero and constant variance σ2. Suppose we observe 4 observations x = (1, 1, −1, −1) and y = (5, 3, 4, 0). (a) Fit the simple linear regression model to this data and report the fitted regression line. (b) Carry out a test of hypotheses using α = 0.05 to determine...
The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. 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...
True or False 1. The correlation coefficient is way to determine if one variable causes another variable to change. 2. A linear model is representation of the linear relationship between two variables. 3. The least squares line, or line of best fit, is the line which minimizes the sum of the individual squares of the residuals. 4. Most linear models do not have any residuals. 5. Regression equations can be used to make predictions. However, the context of the data...
1. What is the coefficient of determination and why is it important? What does it show us? 2. What is heteroskedasticity, which assumption of the linear model does it violate, and how can we test for it? 3. What is multicollinearity? What problems can it cause to our results? 4. If you decide to scale both your dependent and your independent variable by 100, how will your regression results change? 5. Using N=40 observations, you estimate the following model y...
1. Let X and Y be two random variables.Then Var(X+Y)=Var(X)+Var(Y)+2Couv(X,Y). True False 2. Let c be a constant.Then Var(c)=c^2. True False 3. Knowing that a university has the following units/campuses: A, B , the medical school in another City. You are interested to know on average how many hours per week the university students spend doing homework. You go to A campus and randomly survey students walking to classes for one day. Then,this is a random sample representing the entire...
1. For each of the following regression models, write down the X matrix and 3 vector. Assume in both cases that there are four observations (a) Y BoB1X1 + B2X1X2 (b) log Y Bo B1XiB2X2+ 2. For each of the following regression models, write down the X matrix and vector. Assume in both cases that there are five observations. (a) YB1XB2X2+BXE (b) VYBoB, X,a +2 log10 X2+E regression model never reduces R2, why 3. If adding predictor variables to a...