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WorksheetsTUGASAN TOPIK 13
Total questions: 20
Worksheet time: 24mins
What is the equation of the estimated regression line?
Yhat = -53.2073 – 0.1765 X1 + 40.8932 X2 + 0.0126 X3 – 0.4550 X4 + 1.0341 X5 + ε
Y = -53.2073 – 0.1765 X1 + 40.8932 X2 + 0.0126 X3 – 0.4550 X4 + 1.0341 X5
Y = -53.2073 – 0.1765 X1 + 40.8932 X2 + 0.0126 X3 – 0.4550 X4 + 1.0341 X5 + ε
Yhat = -53.2073 – 0.1765 X1 + 40.8932 X2 + 0.0126 X3 – 0.4550 X4 + 1.0341 X5
Yhat = -53.2073 ε – 0.1765 X1 + 40.8932 X2 + 0.0126 X3 – 0.4550 X4 + 1.0341 X5
Interpret the estimated partial slope coefficient of retail gasoline price index.
Assuming other factors constant, when retail gasoline price index increases 1 point, the number of registered new car will decrease by 0.1765 units on average
Assuming other factors constant, when the number of registered new car increases 1 million units, the retail gasoline price index will decrease by 0.1765 point on average
Assuming other factors constant, when retail gasoline price index increases 1 point on average, the number of registered new car will decrease by 176500 units
Assuming other factors constant, when the number of registered new car increases 1 unit, the retail gasoline price index will decrease by 0.1765 million points on average
Assuming other factors constant, when retail gasoline price index increases 1 point, the number of registered new car will decrease by 176500 units on average
Interpret the estimated partial slope coefficient of labor force.
Holding other independent variables constant, for each additional 1% in labor force, the number of registered new car will increase by 1.0341% on average
Holding other independent variables constant, for each additional 1 million in labor force, the number of registered new car will increase by 1.0341 units on average
Holding other independent variables constant, for each additional 1 million units in the number of registered new car, the labor force will increase by 1.0341 million on average
Holding other independent variables constant, for each additional 1 million in labor force, the number of registered new car will increase by 1.0341 million on average
Holding other independent variables constant, for each additional 1% in the number of registered new car, the labor force will increase by 1.0341% on average
Assuming other factors constant, what is the effect of increasing the median price of public transport by 10 cents on the number of registered new car (in units)?
(a)
State the null hypothesis (H0) for the goodness-of-fit test of the model.
β0 = β1 = β2 = β3 = β4 = β5 = 0
β1 = β2 = β3 = β4 = β5 = 0
b1 = b2 = b3 = b4 = b5 = 0
β1 = β2 = β3 = β4 = β5
b0 = b1 = b2 = b3 = b4 = b5 = 0
State the alternative hypothesis (H1) for the goodness-of-fit test of the model.
β0 ≠ β1 ≠ β2 ≠ β3 ≠ β4 ≠ β5 ≠ 0
at least two βi differ
at least one of the βi ≠ 0
β1 ≠ β2 ≠ β3 ≠ β4 ≠ β5 ≠ 0
at least one of the bi ≠ 0
What is the conclusion of the overall significance test of the regression model?
The overall regression model is significant
At least one of the independent variables affect the number of registered new car
The overall regression model fits the data well
The regression model is useful
All the above
Interpret the coefficient of determination.
99.78% of the variation in the number of registered new car could be explained by all the independent variables in the model
99.64% of the variation in the number of registered new car could be explained by all the independent variables in the model
99.64% of the variation in the model is explained by the regression line
99.78% of the variation in all the independent variables is explained by the number of registered new car
The relationship between the number of registered new car and all the independent variables is very strong
Find the value of the standard error of estimate.
(a)
Find the standard error estimate of b4.
(a)
What is the value of the test statistic for b1 ?
(a)
At the 10% level of significance, is the number of registered new cars positively related with per capita disposable income? State the null and alternative hypothesis.
H0 : X3 ≤ 0 ; H1 : X3 > 0
H0 : b3 ≤ 0 ; H1 : b3 > 0
H0 : β3 ≤ 0 ; H1 : β3 > 0
H0 : ρ ≤ 0 ; H1 : ρ > 0
H0 : Y ≤ 0 ; H1 : Y > 0
At the 10% level of significance, is the number of registered new cars positively related with per capita disposable income? What is the decision of the test?
Do not reject H0 because p-value = 0.1368 > α = 0.10
Reject H0 because p-value = 0.1368 > α = 0.05
Reject H0 because p-value = 0.0684 < α = 0.10
Do not reject H0 because p-value = 0.0684 > α = 0.05
None of the above
Which of the followings conclusions are TRUE about the t-test on the partial slope coefficients at 1% level of significance?
I. The number of registered new cars is significantly related to the median price of public transport.
II. The number of registered new cars does not affect the population growth rate.
III. There is a significant relationship between the number of registered new cars and retail gasoline price index.
IV. There is a significant relationship between the labor force and the number of registered new cars.
II and III
I and IV
I, II and IV
I, II, III and IV
In one particular year, the retail gasoline price index is 102 points, the median price of public transport is 150 cents, per capita disposable income is RM17500, labor force and population growth rate are 10 million and 1.5 per cent respectively. Predict the number of registered new cars (in million units).
(a)
Interpret the coefficient of correlation between the retail gasoline price index and the median price of public transport.
There is a negative relationship between retail gasoline price index and median price of public transport
38.2% of the variation in the retail gasoline price index could be explained by the median price of public transport
The relationship between retail gasoline price index and median price of public transport is weak
There is a weak negative relationship between retail gasoline price index and median price of public transport
14.6% of the variation in the median price of public transport could be explained by the retail gasoline price index
Test at the 10% level of significance whether the retail gasoline price index has a significant negative relationship with the median price of public transport. State the null and alternative hypothesis of the test.
H0 : X1 ≥ X2 versus H1 : X1 < X2
H0 : ρ ≥ 0 versus H1 : ρ < 0
H0 : β1 ≥ β2 versus H1 : β1 < β2
H0 : r ≥ 0 versus H1 : r < 0
Test at the 10% level of significance whether the retail gasoline price index has a significant negative relationship with the median price of public transport. What is the value of the test statistic t ?
(a)
Test at the 10% level of significance whether the retail gasoline price index has a significant negative relationship with the median price of public transport. What is the critical value of the test?
(a)
Which of the following statements is TRUE ?
Least-Squares Method produces the “best fit” straight line through the sample data points by minimizing the sum of squares regression
Multiple regression is the process of using several independent variables to predict a number of dependent variables
When an additional independent variable is introduced into a multiple regression model, the coefficient of determination will never decrease
When an additional independent variable is introduced into a multiple regression model, the adjusted coefficient of determination can never decrease
The Y-intercept (b0) represents the predicted value of Y when all independent variables are equal
