A researcher would like to predict the dependent variable YY
from the two independent variables X1X1 and X2X2 for a sample of
N=20N=20 subjects. Use multiple linear regression to calculate the
coefficient of multiple determination and test the significance of
the overall regression model. Use a significance level
α=0.01α=0.01.
X1X1 | X2X2 | YY |
---|---|---|
23.5 | 33.6 | 50.2 |
8.7 | 31.6 | 53.7 |
24.3 | 43 | 43 |
16.7 | 24.6 | 83.6 |
34.2 | 39.1 | 45 |
52.2 | 30 | 55.4 |
32.7 | 41.8 | 34.2 |
24.8 | 20.6 | 71.7 |
31.8 | 44.1 | 51.3 |
46.7 | 52.7 | 17.4 |
19.5 | 23.4 | 81.6 |
18.7 | 46.2 | 48.2 |
52.1 | 47.3 | 54.3 |
34.1 | 6.7 | 81.7 |
64.6 | 36.7 | 41.3 |
63.4 | 57.5 | 17.8 |
83.1 | 44.7 | 31.5 |
44.3 | 27.8 | 43.8 |
56.8 | 42.4 | 22.7 |
55.9 | 49.1 | 37.3 |
SSreg=SSreg=
SSres=SSres=
R2=R2=
F=F=
P-value =
What is your decision for the hypothesis test?
What is your final conclusion?
A researcher would like to predict the dependent variable YY from the two independent variables X1X1...
A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=12N=12 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.01α=0.01. X1X1 X2X2 YY 51.1 40.5 48 53.5 41 51.5 53.2 62.8 42.8 52.3 52.7 51.3 64.1 60 48.8 56.8 62.1 50 61.6 88.1 39.2 60.4 62.5...
A researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N=10 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.02. X1 X2 Y 40.5 62.9 21.8 16.4 51.3 31.8 62.5 44.4 29.6 60.4 53.6 40.6 50.2 54 33.7 39.2 51.5 37 80.9 16.9 58.1 41.6 52.6...
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...
In a multiple regression analysis, two independent variables are considered, and the sample size is 26. The regression coefficients and the standard errors are as follows. b1 = 1.468 Sb1 = 0.89 b2 = −1.084 Sb2 = 0.88 Conduct a test of hypothesis to determine whether either independent variable has a coefficient equal to zero. Would you consider deleting either variable from the regression equation? Use the 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round...
In a multiple regression analysis, two independent variables are considered, and the sample size is 26. The regression coefficients and the standard errors are as follows. b1 = 2.312 Sb1 = 0.81 b2 = −1.950 Sb2 = 0.77 Conduct a test of hypothesis to determine whether either independent variable has a coefficient equal to zero. Would you consider deleting either variable from the regression equation? Use the 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round...
5. Summary of regression between a dependent variable y and two independent variables X, and x2 is as follows. Please complete the table: SUMMARY OUTPUT Regression Statistics Multiple R 0.9620 R Square R2E? Adjusted R Square 0.9043 Standard Error 12.7096 Observations 10 ANOVA F Significance F F=? Overall p-value=? Regression Residual Total 2 df of SSE MS MSR=? MSE? 14052.1550 1130.7450 SSTE? MSE? 9 Coefficients -18.3683 Standard Error 17.9715 t Stat -1.0221 Intercept ty=? 2.0102 4.7378 0.2471 0.9484 P-value 0.3408...
The following ANOVA model is for a multiple regression model with two independent variables: Degrees of Sum of Mean Source Freedom Squares Squares F Regression 2 60 Error 18 120 Total 20 180 Determine the Regression Mean Square (MSR): Determine the Mean Square Error (MSE): Compute the overall Fstat test statistic. Is the Fstat significant at the 0.05 level? A linear regression was run on auto sales relative to consumer income. The Regression Sum of Squares (SSR) was 360 and...