Final stat
If a data set contains 6 independent variables, the number of all possible regression models will be __________.
63
A real estate analyst has developed a multiple regression line, y = 63 + 0.187 x1 - 3.7 x2, to predict y = the market price of a home (in $10,000s), using independent variables, x1 = the total number of square feet of living space, and x2 = the age of the house in years. What does the regression coefficient of x2 suggest?
If the square feet area of living space is kept constant, a 1 year increase in the age of the homes will result in a predicted increase of $37,000 in the price of the homes.
A stepwise regression search procedure stops when _____________________.
no more significant independent variables remain outside of the model
One of the assumptions of simple regression analysis is that the error terms are exponentially distributed. t/f
false
Assume that X1, X2 and X3 are the dollars invested in three different common stocks from New York Stock Exchange. In order to diversify the investments, the investing company requires that no less than 60% of the dollars invested shall be in ʺstock 1 and stock 3 combinedʺ. The constraint for this requirement can be written as:
0.4X1-0.6X2+0.4X3 ≥ 0
Cully Turniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the storage space constraint?
100 B + 90 M <= 18000
The production manager for the Cully soft drink company is considering the production of two kinds of soft drinks: regular (R) and diet(D). Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint?
2R + 4D <= 480
Dr. Chiang works at Georgia Southern for a period of time. He has taught various number of students in each semester. Assume in the most recent 7 semesters, he has taught, from most recent to the earliest, 102 (current semester), 97 (the semester before the current semester), 86, 99, 101, 95, 97 students, respectively. Use 4-period simple moving average method, please tell Dr. Chiang how many students will he teach in next semester?
96
Dr. Chiang works at Georgia Southern for a period of time. He has taught various number of students in each semester. Assume in the most recent 7 semesters, he has taught, from most recent to the earliest, 102 (current semester), 97 (the semester before the current semester), 86, 99, 101, 95, 97 students, respectively. Use 3-period weighted moving average method with the weight 4 for most recent period, weight 3 for second most recent period, and weight 1 for least recent period. Please tell Dr. Chiang how many students will he teach in next semester?
98.125
Dean Air uses a linear programming model to schedule flights, assign crews and meet passenger demand. The objective function is to minimize downtime. Constraints include a limit on pilot hours, meeting passenger demand, and scheduled downtime. Which of the following cannot be accomplished with sensitivity analysis?
Change the objective to maximize profits.
Which of the following statement about using Excel on multiple linear regression is WRONG?
F-test is the first test we should make.
An extremely strong correlation between variable X and Y means that the variation of X causes the variation of Y. t/f
False
The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. Which of the following describe the right objective function of maximized profit?
Max P = 2A + B
The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular (R) and diet (D). Two of her limited resources are production time (8 hours per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What are the optimal daily production quantities of each product and the optimal daily profit?
R = 90, D = 75, Z = $420
In March 2016, HTC sold 756 flagship phones, HTC One, in USA. Dr. Chiang predicted that HTC would sell 637 HTC One phones for that time period. If Dr. Chiang uses simple exponential smoothing method to forecast the number of HTC One sales using an alpha value equal 0.85, what is the forecasted HTC Once sales in April 2016?
The forecasted number of HTC One sales in April 2016 is greater than 693 but less than or equal to 746.
What is the coordinate value of the intersection point of the following two line equations. Equation 1: 5X1 - 4X2 = 6 Equation 2: 3X1 + 7X2 = 13
X1 = 2 X2 = 1
What is the coordinate value of the intersection point of the following two line equations. Equation 1: 4X1 - 3X2 = 26 Equation 2: 5X1 + 6X2 = 13
X1 = 5 X2 = -2
An intern sets up a linear program to optimize the use of paper products in the men's washroom. The system of equations he develops is: Max objective = 2T + 3S + 4ST subject to 3T + 6S <= 40 10T + 10S <= 66 10T + 15S <= 99 His mentor studies the model, frowns, and admonishes the intern for violating which of the following properties of linear programming models?
additivity
A linear programming model consists of
constraints, an objective function, and decision variables
"Range of optimality" describes the impact of simultaneous changes in objective function values and right-hand-side values. t/f
false
A non-binding constraint is always a redundant constraint. t/f
false
An extreme point is an optimal solution. t/f
false
Each decision variable must appear in at least two constraints. t/f
false
If the correlation coefficient between two variables is -1, it means that the two variables are not related. t/f
false
Minimization linear programming models may not involve "<=" constraints. t/f
false
The complementary slackness principle states that either there is zero slack on a constraint or the reduced cost is zero. t/f
false
The mean square error (MSerr) is calculated by dividing the sum of squares error (SSerr) by the number of independent variable considered in the model (K). t/f
false
The slope of the regression line, y = 98 − 5x, is 98. t/f
false
The strength of a linear relationship between two variables changes if the units of the data are converted, say from feet to inches. t/f
false
Time-series data are data gathered on a desired characteristic at a particular point in time. t/f
false
If we reject H0: β1= β2= 0 using the F-test, then we should conclude that at least one of the slope is different from zero. t/f
fasle
The slope of the regression line, y = 17 − 8x, is 8. t/f
fasle
For a maximization problem, the shadow price measures the ________ in the value of the optimal solution, per unit increase for a given ________.
improvement, resource
Multiple optimal solutions (alternate solution) can occur when the objective function is ________ a constraint line.
parallel to
The adjusted R2 accounts for ___________________________________.
the number of independent variables in the model
A qualitative variable which represents categories such as geographical territories or job classifications may be included in a regression model by using indicator or dummy variables. t/f
true
Certainty assumption means that the value of the coefficient of a linear programming model is known. t/f
true
Correlation is a measure of the degree of linear relationship between two variables. t/f
true
If the variance inflation factor is bigger than 10, the regression analysis might suffer from the problem of multicollinearity. t/f
true
If two extreme points are optimal, then so is every point on the line segment connecting the two extreme points. t/f
true
In the multiple regression model y = beta0 + beta1x1 + beta2x2 + beta3x3 + epsilon, the beta coefficients of the x variables are called partial regression coefficients. t/f
true
On a coordinate system, if the X1 variable is made on the horizontal axis, equation X1 = 3 means a vertical line. t/f
true
Regression analysis with one dependent variables and at least one nonlinear independent variables is called multiple regression. t/f
true
Regression models in which the highest power of any predictor variable is 1 and in which there are no cross product terms are referred to as first-order models. t/f
true
Stepwise regression is one of the ways to prevent the problem of multicollinearity. t/f
true
The mean square error (MSerr) is calculated by dividing the sum of squares error (SSerr) by degrees of freedom of the regression (dfreg). t/f
true
When specifying linear constraints, the modeler must take into account the unit specification of the decision variables so that the units represented by the left side of the constraints are consistent with the units represented by the right side of the constraints. t/f
true
You are currently paying $12 per hour for labor, and labor costs are included in the calculation of the objective function coefficients of a maximization problem. The shadow price for labor printed on the sensitivity analysis report is $8. It would be economically beneficial to you if you could secure extra labor for $15 per hour. t/f
true
