a:
Regression equation.
a:
Explanation of Solution
The general regression equation can be written as follows:
The term
Table 1 shows the processing of data as follows:
Table 1
Sl | |||||
1 | -5 | 15 | 25 | 225 | -75 |
2 | -2 | 9 | 4 | 81 | -18 |
3 | 0 | 7 | 0 | 49 | 0 |
4 | 3 | 6 | 9 | 36 | 18 |
5 | 4 | 4 | 16 | 16 | 16 |
6 | 7 | 1 | 49 | 1 | 7 |
Total | 7 | 42 | 103 | 408 | -52 |
Standard deviation
Standard deviation is -202.2.
The variance of x
The variance of x is 18.97.
The value of coefficient ( b1) can be calculated as follows:
The value of b1 is -1.065.
The average value
The average value of x is 1.167.
The average value
The average value of x is 7.
Intercept b0 can be calculated as follows:
The intercept value is 8.253.
Thus, the regression equation is given below:
b:
The predicted value of y.
b:
Explanation of Solution
The estimated value of y
Table 2 shows the predicted value of x that is obtained using the regression equation with different levels of x values as follows:
Table 2
Sl | ||
1 | -5 | 13.58 |
2 | -2 | 10.38 |
3 | 0 | 8.253 |
4 | 3 | 5.058 |
5 | 4 | 3.993 |
6 | 7 | 0.758 |
c:
Calculate the residual.
c:
Explanation of Solution
The value of residual
Table 3 shows the residual value that is obtained using Equation (1) as follows:
Table 3
Sl | |||
1 | -5 | 13.58 | 1.42 |
2 | -2 | 10.38 | -1.38 |
3 | 0 | 8.253 | -1.253 |
4 | 3 | 5.058 | 0.942 |
5 | 4 | 3.993 | 0.007 |
6 | 7 | 0.758 | 0.202 |
d:
Calculate the standardized residual.
d:
Explanation of Solution
The variance of y
The variance of y is 22.8.
Error sum of square (SSE) can be calculated as follows:
Error sum of square is 6.451.
The value of
The value of
The value of standardized residual (se) can be calculated using the below equation:
Table 5 shows the standardized residual value that is obtained using Equation (2) as follows:
Table 5
Sl | se | |||
1 | -5 | 13.58 | 1.42 | 1.18 |
2 | -2 | 10.38 | -1.38 | -1.087 |
3 | 0 | 8.253 | -1.253 | -0.987 |
4 | 3 | 5.058 | 0.942 | 0.742 |
5 | 4 | 3.993 | 0.007 | 0.0055 |
6 | 7 | 0.758 | 0.202 | 0.159 |
e:
Identification of outliers.
e:
Explanation of Solution
From the above calculations, it is known that there are no outliers.
Want to see more full solutions like this?
Chapter 16 Solutions
Statistics for Management and Economics (Book Only)
- Consider the simple regression model: y=0.56+1.56x+u Using this and assuming the estimated Var(y)=0.64 and the estimated Var(x)=3.07, what is the estimated Var(x+y)?arrow_forwardGiven the regression equation Y = 100 + 10X a. What is the change in Y when X changes by +3? b. What is the change in Y when X changes by -4? c. What is the predicted value of Y when X = 12? d. What is the predicted value of Y when X = 23? e. Does this equation prove that a change in X causes a change in Y?arrow_forwardPlease no written by hand The assumption of normally distributed errors means that... A. errors can be ignored when doing regression modelling. B. the OLS estimators can also be assumed to be normally distributed since they are a linear functions of the errors. C. the OLS estimators can also be assumed to be normally distributed since they are BLUE. D. the OLS estimators can also be assumed to be normally distributed since they are minimum variance. E. the regression model will not be subject to specification error.arrow_forward
- The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x1) and newspaper advertising (x2). The estimated regression equation was ŷ = 83.7 + 2.23x1 + 1.60x2. The computer solution, based on a sample of eight weeks, provided SST = 25.4 and SSR = 23.445. (a)Compute and interpret R2 and Ra2.(Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (??) . Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (??).arrow_forwardIn general, what is true about the relationship between the Sum of Squared Residuals in the restricted and unrestricted model? a. SSRr = R-squared * SSRur b. SSRr < SSRur c. SSRr > SSRur d. SSRr = SSRurarrow_forwardIf a regression equation contains an irrelevant variable, the parameter estimates will be Select one: a. Consistent and unbiased but inefficient b. Consistent and asymptotically efficient but biased c. Consistent, unbiased and efficient. d. Inconsistentarrow_forward
- DEPENDENT VARIABLE Qc R- SQUARE P- VALUE ON F 64 0.8093 0.0001 INDEPENDENTVARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 8.20 4.01 2.04 0.0461 PC -3.54 1.64 -2.16 0.0357 M 0.64287 0.19 3.38 0.0014 PA 0.7854 0.38 2.07 0.0439 10. Write the resulting regression equation. Q = f( P, M, PR) where Qc = demand for cement/month (in yards) Pc = the price of cement per yard, M = country’s tax revenues per capita, and PR = the price of asphalt per yard.arrow_forwardRequired: i)Based on the data, construct the sample regression function (SRF). ii)Compute the variance for β0 and β1. iii)Compute the standard error for β0 and β1.arrow_forwardThe standard deviation of the error terms in an estimated regression equation is known as:arrow_forward
- What is the model constant when the dummy variable equals 1 in the following equations, where x1 is a continuous variable and x2 is a dummy variable with a value of 0 or 1? a. Ŷ = 4 + 8x1 + 3x2 b. Ŷ = 7 + 6x1 + 5x2 c. Ŷ = 4 + 8x1 + 3x2 + 4x1x2arrow_forward1. You are running a probability regression. If your data contains many outliers, you’d be better off using (A) A linear probability model. (B) Probit. (C) Logit. (D) Either probit or logit would work fine. (E) Any of the above regression models would work fine.arrow_forward4. From the regression output, report the coefficients, standard errors, t-statistics, probability and R-squared (report the results in a table). 5. Re-write the specified model in (a) with values from the regression results and interpret the coefficients.arrow_forward
- Managerial Economics: Applications, Strategies an...EconomicsISBN:9781305506381Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. HarrisPublisher:Cengage Learning