1.
When testing r linear restrictions imposed on the model y = β0 + β1x1 + ... + βkxk + ε, the test statistic is assumed to follow the F(df1, df2) distribution with ____________________.
df1 = k and df2 = n – k – 1
df1 = k – 1 and df2 = n – k – 1
df1 = r and df2 = n – k
df1 = r and df2 = n – k – 1
2.
(Round all intermediate calculations to at least 4 decimal places.) |
Consider the following sample regressions for the linear, the quadratic, and the cubic models along with their respective R2 and adjusted R2. |
Linear | Quadratic | Cubic | |
Intercept | 9.45 | 9.78 | 9.84 |
x | 2.60 | 2.69 | 1.79 |
x2 | NA | −0.30 | −0.32 |
x3 | NA | NA | 0.25 |
R2 | 0.790 | 0.818 | 0.877 |
Adjusted R2 | 0.791 | 0.815 | 0.876 |
a. |
Predict y for x = 2 and 3 with each of the estimated models. (Round your answers to 2 decimal places.) |
Linear yˆy^ | Quadratic yˆy^ | Cubic yˆy^ | |
x = 2 | |||
x = 3 | |||
b. | Select the most appropriate model. | ||||||
|
1.
When testing r linear restrictions imposed on the model y = β0 + β1x1 + ... + βkxk + ε, the test statistic is assumed to follow the F(df1, df2) distribution with df1 = r and df2 = n – k – 1
1. When testing r linear restrictions imposed on the model y = β0 + β1x1 +...
1. When testing r linear restrictions imposed on the model y = β0 + β1x1 + ... + βkxk + ε, the test statistic is assumed to follow the F(df1, df2) distribution with ____________________. df1 = k and df2 = n – k – 1 df1 = k – 1 and df2 = n – k – 1 df1 = r and df2 = n – k df1 = r and df2 = n – k – 1 2. (Round...
Consider the following sample regressions for the linear, the quadratic, and the cubic models along with their respective R2 and adjusted R2. Linear Quadratic Cubic Intercept 9.66 10.00 10.06 x 2.66 2.75 1.83 x2 NA −0.31 −0.33 x3 NA NA 0.26 R2 0.810 0.836 0.896 Adjusted R2 0.809 0.833 0.895 a. Predict y for x = 1 and 2 with each of the estimated models. (Round intermediate calculations and final answers to 2 decimal places.) b. Select the most appropriate...
Consider the following sample regressions for the linear, the quadratic, and the cubic models along with their respective R2 and adjusted R2. Intercept х x2 Linear 28.53 0.12 NA NA Quadratic 28.80 0.01 0.01 Cubic 28.62 0.15 -0.02 -0.01 x3 NA R2 Adjusted R2 0.005 -0.021 0.006 -0.048 0.006 -0.077 a. Predict y for x = 2 and 4 with each of the estimated models. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal...
(Round all intermediate calculations to at least 4 decimal places.) Consider the following sample regressions for the linear, the quadratic, and the cubic models along with their respective R2 and adjusted R2. Linear Quadratic Cubic Intercept 25.97 20.73 16.20 x 0.47 2.82 6.43 x2 NA −0.20 −0.92 x3 NA NA 0.04 R2 0.060 0.138 0.163 Adjusted R2 0.035 0.091 0.093 pictureClick here for the Excel Data File a. Predict y for x = 3 and 5 with each of the...
1. Consider the following simple regression model: y = β0 + β1x1 + u (1) and the following multiple regression model: y = β0 + β1x1 + β2x2 + u (2), where x1 is the variable of primary interest to explain y. Which of the following statements is correct? a. When drawing ceteris paribus conclusions about how x1 affects y, with model (1), we must assume that x2, and all other factors contained in u, are uncorrelated with x1. b....
Using the appropriate model, sample size n, and output below: Model: y = β0 + β1x1 + β2x2 + β3x3 + ε Sample size: n = 16 Regression Statistics Multiple R 0.9975 R Square 0.9950 Adjusted R Square 0.9937 Standard Error 440.3187 Observations 16 ANOVA DF SS MS F Significance F Regression 3 461,801,144.1072 153,933,714.7024 793.9616 0.0000 Residual 12 2,326,566.6701 193,880.5558 Total 15 464,127,710.7773 (1) Report the total variation, unexplained variation, and explained variation as shown on the output. (Round...
31. Suppose you fit a multiple linear regression model y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + ε to n = 30 data points and obtain SSE = 282 and R^2 = 0.8266 a.) Find an estimate of s^2 for the multiple regression model (a) s^2 ≈ 30.9856 (b) s^2 ≈ 28.6021 (c) s^2 ≈ 1.3111 (d) s^2 ≈ 29.7938 (d) b.) Based on the data information given in a.), you use F-test to test H0...
Consider the sample regressions for the linear (Model 1), the logarithmic (Model 2), the exponential (Model 3), and the log-log (Model 4) models. For each of the estimated models, predict y when x equals 50. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Response Variable: y Response Variable: In(y) Model 18.52 1.68 NA 23.92 Model 2 -6.74 NA 29.96 19.71 Model 3 1.48 0.06 NA 0.12 Model 4 1.02 NA 0.96 0.10 Intercept In(x) 102.52 Model...
1. In order to test whether the multiple linear regression model y bo +b,x1 + b2X2 is better than the average model (lazy model), which of the following null hypotheses is correct: a. Ho' b1 = b2 = 0 Но: B1 B2-0 с. We have a dataset Company with three variables: Sales, employees and stores. To build a multiple linear regression model using Sales as dependent variable, number of stores and number of employees as independent variables, which of the...
(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...