500 câu trắc nghiệm Kinh tế lượng – 9C

Find the explained variation for the paired data.
14) The paired data below consists of heights and weights of 6 randomly selected adults. The \(\hat y\) = -181.342 + 144.46x. Find the explained variation.

● 979.44
○ 1149.2
○ 100.06
○ 1079.5

Construct the indicated prediction interval for an individual y.
15) The paired data below consists of heights and weights of 6 randomly selected adults. The equation of the regression line is \(\hat y\) = -181.342 + 144.46x and the standard error of estimate is se = 5.0015. Find the 95% prediction interval for the weight of a person whose height is 1.75 m.

○ 65.4 < y < 77.6
○ 58.5 < y < 84.5
● 56.5 < y < 86.5
○ 52.1 < y < 90.9

Use computer software to find the regression equation. Can the equation be used for prediction?
16) A wildlife analyst gathered the data in the table to develop an equation to predict the weights of bears. He used WEIGHT as the dependent variable and CHEST, LENGTH, and SEX as the independent variables. For SEX, he used male=1 and female=2.

○ WEIGHT = 196 + 2.35CHEST + 3.40LENGTH + 25SEX;
Yes, because the R2 is high
○ WEIGHT = 442.6 + 12.1CHEST + 4.2LENGTH – 21SEX;
Yes, because the P-value is low
○ WEIGHT = -320 + 10.6CHEST + 7.3LENGTH – 10.7SEX;
Yes, because the P-value is high
● WEIGHT = -442.6 + 12.1CHEST + 3.6LENGTH – 23.8SEX;
Yes, because the adjusted R2 is high

Use computer software to obtain the regression and identify R2, adjusted R2, and the P-value.
17) An anti-smoking group used data in the table to relate the carbon monoxide of various brands of cigarettes to their tar and nicotine content.

○ .976, .921, .002
○ .931, .902, .000
○ .861, .900, .015
● .943, .934, .000

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Use computer software to obtain the regression equation. If the accompanying statistics confirm use of the equation for prediction, use the estimated equation to find the predicted value; otherwise, explain why the equation should not be used.
18) A study of food consumption in the country related the level of food consumed to an index of food prices and an index of personal disposable income. Next year, the income index number is expected to be 100.2, and the price index is expected to be 108.3. These numbers would indicate a predicted value for food consumption.

The regression equation is \(\hat y\) = 57.7 + 0.153×1+ 0.270×2. Since the adjusted coefficient of determination is 85.2% and the P-value is 0.0000, the regression equation can be used for prediction. The predicted food consumption is 102.3.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use computer software to find the best regression equation to explain the variation in the dependent variable, Y, in terms of the independent variables, X1, X2, X3.

19)

CORRELATION COEFFICIENTS: Y/ X1 = .951; Y/ X2 = .789; Y/ X3 = -.616
COEFFICIENTS OF DETERMINATION: Y/ X1 = .905; Y/ X1, X2 = .919; Y/ X1, X2, X3 = .927
○ \(\hat y\) = -412 + 13.6X1 + 3.15X2
○ \(\hat y\) = -543 + 12.8X1 + 4.15X2
● \(\hat y\) = -355 + 14.9X1
○ \(\hat y\) = -442 + 12.1X1 + 3.58X2 -23.8X3

Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model
is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several models and compare the values of R2.
20) The table below shows the population of a city (in millions) in each year during the period 1990 – 1995. Using the number of years since 1990 as the independent variable, find the regression equation of the best model.

○ y = 1.27\({x^{{\rm{0}}{\rm{.550}}}}\)
● y = 1.08\({{\rm{e}}^{{\rm{0}}{\rm{.228x}}}}\)
○ y = 0.930 + 0.454x
○ y = 0.05\({x^2}\) + 0.27x + 1.06