Stat and Optimization
in a regression equation, y = 49.56 + .97x the slope is___?
0.97
A manager wishes to predict the annual cost (y) of an automobile based on the number of miles (x) driven. The following model was developed: y = 2,000 + 0.42x. If a car is driven 20,000 miles, the predicted cost is ____________.
10,400
The following regression model was fitted to sample data with 12 observations: y Overscript ̂ EndScripts= 30 + 4.50x. What is the change in the predicted value of y for a unit change in the value?
4.50
A simple regression model developed for 12 pairs of data resulted in a sum of squares of error, SSE = 246. The standard error of the estimate is _______.
4.96
For a certain data set the regression equation is y = 29 - 5x. The correlation between y and x in this data set ____? A. is negative B. is positive C. must be > 1 D. must be 1 E. must be 0
A. is negative
Which of the following equations represents a linear relationship between y and x? (Note: m and b are constants.) A. y = m /x + b B. y = m x2 C. y = m x + b D. y = m b
C. y = m x + b
The coefficient of correlation in a simple regression analysis is = - 0.6. The coefficient of determination for this regression would be _______. A.0.6 B. - 0.6 or + 0.6 C. - 0.36 D. 0.13 E. 0.36
E. 0.36
a cost accountant is developing a regression model to predict the total cost of producing a batch of printed circuit boards as a linear function of batch size (the number of boards produced in one lot or batch). The intercept of this model is the ____? A. batch size B. unit variable cost C. fixed cost D. total variable cost E. total cost
E. fixed cost
If the standard error of the estimate for a regression model fitted to a large number of paired observations is 1.75, approximately 68% of the residuals would lie within ______ A. −0.95 and +0.95 B. −3.50 and +3.50 C. −0.97 and +0.97 D. −0.68 and +0.68 E. −1.75 and +1.75
E. −1.75 and +1.75
T/F Data points that lie apart from the rest of the points are called deviants.
False
T/F In a simple regression the coefficient of correlation is the square root of the coefficient of determination.
False
T/F In regression, the variable that is being predicted is usually referred to as the independent variable.
False
T/F In the simple regression model, y = 21 − 5x, if the coefficient of determination is 0.81, we can say that the coefficient of correlation between y and x is 0.90.
False
T/F One of the assumptions of simple regression analysis is that the error terms are exponentially distributed
False
T/F The proportion of variability of the dependent variable (y) accounted for or explained by the independent variable (x) is called the coefficient of correlation.
False
T/F The range of admissible values for the coefficient of determination is −1 to +1.
False
T/F The slope of the regression line, y = 21 − 5x, is 5.
False
T/F The standard error of the estimate, denoted se, is the square root of the sum of the squares of the vertical distances between the actual Y values and the predicted values of Y.
False
T/F The strength of a linear relationship in simple linear regression change if the units of the data are converted, say from feet to inches.
False
T/F The variability in the estimated slope is smaller when the x-values are more spread out.
False
T/F When the slope of a simple linear regression equation is a negative value, the correlation coefficient can be either positive or negative.
False
Another name for an F test
Hypothesis test
Formula for se
Sq Root of (SSE / n-2)
Which of the following is not an assumption of the regression model?
The error terms are independent
T/F A procedure used for finding the equation of a straight line that provides the best fit by minimizing the sum of the squared vertical distances of points from the line is called the least squares method.
True
T/F A t-test is used to determine whether the coefficients of the regression model are significantly different from zero.
True
T/F Correlation is a measure of the degree of linear relationship between two variables.
True
T/F For the regression line, y = 21 − 5x, 21 is the y-intercept of the line.
True
T/F Given x, a 95% prediction interval for a single value of y is always wider than a 95% confidence interval for the average value of y.
True
T/F If the correlation coefficient between two variables is -1, it means that the two variables are not related.
True
T/F In a simple linear regression, the least squares line turns out to be y = 120 + 4x. The sum of the residuals (errors) around this line will be 0.
True
T/F In simple linear regression analysis, when testing for significance, the F test and the t test will always result in the same conclusion.
True
T/F In simple regression analysis the error terms are assumed to be independent and normally distributed with zero mean and constant variance.
True
T/F Regression output from Excel software directly shows the regression equation.
True
T/F Regression output from Excel software includes an ANOVA table.
True
T/F Residual analysis makes use of a plot of residuals (on the y axis) and the independent variable (on the x axis) to evaluate the assumptions about the error term in regression.
True
T/F The difference between the actual y value and the predicted y value found using a regression equation is called the residual.
True
T/F The first step in simple regression analysis usually is to construct a scatter plot.
True
T/F The process of constructing a mathematical model or function that can be used to predict or determine one variable by another variable is called regression analysis.
True
T/F The standard error of estimate (Se) in simple linear regression is the square of the Mean Square Error (MSE) which is the sum of squares error (SSE) multiplied by its degrees of freedom n-2.
True
T/F To determine whether the overall regression model is significant, the F-test is used.
True
B1 is associated with
Y intercept
The numerical value of the coefficient of correlation must be _______.
between -1 and +1
The numerical value of the coefficient of determination must be _______.
between 0 and 1
The proportion of variability of the dependent variable accounted for or explained by the independent variable is called the _______.
coefficient of determination
A quality manager is developing a regression model to predict the total number of defects as a function of the day of week the item is produced. Production runs are done 10 hours a day, 7 days a week. the explanatory variable is ____?
day of week
another name for response variable
dependent
A hospital administrator developed a regression line, y = 30 + 2x, to predict y = the number of full-time employees (FTE) needed using x = the number of beds. The slope of this regression line suggests this: __________.
for a unit increase in the number of beds, the number of FTEs is predicted to increase by 2
if alpha < PV
ftr Ho
The assumption of constant error variance in regression analysis is called _______.
homoscedasticity
Another name for explanatory variable
independent
The values of b0 and b1 in a regression equation are determined using sample data through a process called __________.
least squares analysis
If there is a perfect negative correlation between two sets of numbers, then ____?
r = -1
If there is a positive correlation between two sets of number, then____?
r > 0
The process of constructing a mathematical model that can be used to predict one variable using another variable or other variables is called __________.
regression analysis
If PV < alpha
reject Ho
actual Y - estimated y = ___?
residuals
Least squares regression line is one that __________.
results in the smallest sum of errors squared
A standard deviation of the error of the regression model is called the _______.
standard error of the estimate
The total of the squared residuals is called the _______.
sum of squares of error
If x and y in a regression model are totally unrelated, _______.
the coefficient of determination would be 0
One of the assumptions made in simple regression is that ______________.
the error terms are normally distributed
B0 is associated with
x
