Question

Format L 01 X ✓ fx K L M N C X2 15 Question 14: Note that Y represents the dependent variable and X1-X3 represent 3 (quantitative) independent variables. Let a=0.05. A Y 155 168 147 192 134 152 B X1 99.43 99.67 97.95 99.97 97.16 98.62 97.32 97.99 98.79 99.26 99.63 97.86 98.97 97.81 99.23 D X3 0.56 0.62 0.49 0.75 0.29 0.51 0.13 0.48 0.62 0.68 0.71 0.19 0.62 0.27 (a) Write out the estimated regression line (including all variables). Answer: yhat = (b) What is the adjusted coefficient of determination? Answer: (c) Predict Y for X1 = 99.01, X2 = 21, and X3 = 0.65. 129 144 Answer: 158 169 175 134 158 136 168 0.67 (d) Run an overall Ftest to determine if the multiple regression model is significant. To receive full credit you must give me: (i) Test Statistic Answer: (ii) P-value Answer: (iii) Decision: Reject or Fail to Reject Ho? Answer: (e) Should the y-intercept be removed from the model? Give me the p-value that supports your answer. Answer: (f) Should any of the independent variables (X1, X2, X3) be removed from the model? Give me the p-values that support your answer. Answer:

Answer 1

EXCEL (Data Analysis) output:

SUMMARY OUTPUT Regression Statistics Multiple R 0.969144415 R Square 0.939240898 Adjusted R Square 0.922670234 Standard Error 4.947543344 Observations 15 ANOVA Significance F 5.61004E-07 Regression Residual Total 3 11 14 SS MS F 4162.339963 1387.446654 56.68094 269.2600366 24.47818515 4431.6 Intercept Coefficients Standard Error Stat p-value Lower 95% Upper 95% -1170.251659 350.2934082 -3.340775565 0.006584 -1941.242251 -399.2610661 13.17170556 3.603806722 3.654942281 0.003788 5.239780452 21.10363067 0.634707872 0.324290725 1.957218702 0.076175 -0.079051201 1.348466946 23.55113227 17.69695706 1.330801233 0.210181 -15.39960757 62.50187211 X2 X3 The estimated regression equation is ĝ=-1170.2517 +13.1717 X1 +0.6347 X2 + 23.5511X3 - (6)

The value of adjusted coefficient of determination is R =0.9227. û =-1170.2517+13.1717X, +0.6347X2 +23.5511X; =-1170.2517+13.1717 (99.01)+0.6347 (21)+23.5511(0.65) =-1170.2517+1304.1300+13.3287 +15.3082 = 162.5152 (d) (1). Test Statistic: 56.6809. (ii). P-value = 0 (iii). Reject H -

No, the y-intercept should not be removed from the model. P-value = 0.0066. The independent variables X, and X, should be removed. P-value for X2 = 0.0762. P-value for X, = 0.2102.