12.1 Correlation and Regression Flashcards
A company has accumulated data for the last 24 months in order to determine if there is an independent variable that could be used to estimate shipping costs. Three possible independent variables being considered are packages shipped, miles shipped, and pounds shipped. The quantitative technique that should be used to determine whether any of these independent variables might provide a good estimate for shipping costs is
A. Flexible budgeting
B. Linear regression
C. Linear programming
D. Variable costing
B. Linear regression
Regression analysis is also called
least-squares analysis
The process of deriving the linear equation that describes the relationship between two (or more) variables with a nonzero coefficient of correlation
Regression analysis
In the standard regression equation y = a + bx, the letter b is best described as a(n)
A. Independent variable.
B. Dependent variable.
C. Constant coefficient.
D. Variable coefficient.
D. Variable coefficient.
In the standard regression equation, b represents the variable coefficient. For example, in a cost determination regression, y equals total costs, b is the variable cost per unit, x is the number of units produced, and a is fixed cost.
Also a slope.
In the standard regression equation y=a+bx, the letter a is best described as
The y-intercept
In the standard regression equation y=a+bx, the letter x is best described as
the independent variable
The results of regressing y against x are as follows:
Coefficient
Intercept: 5.23
Slope: 1.54
When the value of x is 10, the estimated value of y is
A. 20.63
B. 53.84
C. 8.05
D. 6.77
A. 20.63
A simple regression can be calculated using the formula for a straight line:
y = a + bx
Where: y = the dependent variable
a = the y-axis intercept
b = the slope of the regression line
x = the independent variable
Solving with the information given yields the following results:
y = a + bx
= 5.23 + (1.54 × 10)
= 5.23 + 15.4
= 20.63
A nationwide retail mattress firm will begin selling high-end crib mattresses next year. Management believes sales for this product will be driven primarily by birth rates but will be influenced to a lesser extent by income levels. The best method to use to predict next year’s sales is
A. Time-series regression.
B. Multiple regression.
C. Simple regression.
D. Maximum likelihood regression.
B. Multiple regression.
Management believes sales will be driven by birthrates and, to a lesser extent, income levels, which matches the multiple regression method. Multiple regression is used when there is more than one independent variable. The two independent variables are (1) birthrates and (2) income levels.
Alpha Company produces several different products and is making plans for the introduction of a new product, which it will sell for $6 a unit. The following estimates have been made for manufacturing costs on 100,000 units to be produced the first year:
Direct materials: $500,000
Direct labor: $40,000 (the labor rate is $4/hour)
Overhead costs have not been established for the new product, but monthly data on total production and overhead cost for the past 24 months have been analyzed using simple linear regression. The results below were derived from the simple regression and provide the basis for overhead cost estimates for the new product.
Dependent variable (y) – Factory overhead costs
Independent variable (x) – Direct labor hours
Computed values:
y intercept: $40,000
Coefficient of independent variable: $2.10
Coefficient of correlation: 0.953
Standard error of estimate: $2,840
Standard error of regression coefficient: 0.42
Mean value of independent variable: $18,000
Coefficient of determination: 0.908
Alpha’s total overhead cost for an estimated activity level of 20,000 direct labor hours would be
A. $222,000
B. $82,000
C. $122,000
D. $42,000
B. $82,000
The total overhead may be estimated using the regression equation as y = a + bx.
Total overhead
= $40,000 + [($2.10) × (20,000)] = $82,000
Fixed costs are $40,000 and variable costs are $2.10 per direct labor hour.
A company uses regression analysis in which monthly advertising expenses are used to predict monthly product sales, both in millions of dollars. The results show a regression coefficient for the independent variable equal to 0.8. This coefficient value indicates that
A. Advertising is not a good predictor of sales because the coefficient is so small.
B. The average monthly advertising expenditure in the sample is $800,000.
C. On average, every additional dollar of advertising results in $0.8 of additional sales.
D. When monthly advertising is at its average level, product sales will be $800,000.
C. On average, every additional dollar of advertising results in $0.8 of additional sales.
In the standard regression equation y = a + bx, b represents the change in the dependent variable corresponding to a unit change in the independent variable. Thus, it is the slope of the regression line.
A manufacturer developed the following multiple regression equation, utilizing many years of data, and uses it to model, or estimate, the cost of its product.
Cost = FC + (a × L) + (b × M)
Where: FC = fixed costs
L = labor rate per hour
M = material cost per pound
Which one of the following changes would have the greatest impact on invalidating the results of this model?
A. Renegotiation of the union contract calling for much higher wage rates.
B. A significant reduction in factory overheads, which are a component of fixed costs.
C. A large drop in material costs, as a result of purchasing the material from a foreign source.
D. A significant change in labor productivity.
D. A significant change in labor productivity.
In multiple regression, a large difference between the expected value and the actual value of one of the coefficients has the most impact in rendering the model invalid. A change in costs would be incorporated into the equation automatically, but a change in productivity per hour would not.
In order to analyze sales as a function of advertising expenses, the sales manager developed a simple regression model. The model included the following equation, which was based on 32 monthly observations of sales and advertising expenses with a related coefficient of determination of .90.
Sales = $10,000 + (2.5 × Advertising expenses)
If the advertising expenses in 1 month amounted to $1,000, the related point estimate of sales would be
A. $12,500
B. $11,250
C. $12,250
D. $2,500
A. $12,500
The simple regression equation can be solved as follows:
Sales = $10,000 + (2.5 x Advertising expenses)
= $10,000 + (2.5 x $1,000)
= $10,000 + $2,500
= $12,500
결정 계수 𝑅2=0.90 은 독립 변수들이 종속 변수의 변동을 90% 설명한다는 뜻이며, 이는 대체로 데이터의 설명력이 높은 모델임을 나타냅니다.
