OIS 3440 Final Exam (Ch 14/15)
In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240. The adjusted coefficient of determination is
0.66
(National automotive magazine) Based on this output and your understanding of multiple regression analysis, how many degrees of freedom are associated with the Residual in the ANOVA table?
22
A forecasting model of the following form was developed: y = B0 + B1xj + B2 + B3 + ε Which of the following best describes the form of this model?
3rd degree polynomial model
If a decision maker wishes to develop a regression model in which the University Class Standing is a categorical variable with 5 possible levels of response, then he will need to include how many dummy variables?
4
A decision maker is considering including two additional variables into a regression model that has as the dependent variable, Total Sales. The first additional variable is the region of the country (North, South, East, or West) in which the company is located. The second variable is the type of business (Manufacturing, Financial, Information Services, or Other). Given this, how many additional variables will be incorporated into the model?
6
Use the following regression results to answer the question below. How many observations were involved in this regression?
8
Which of the following would best describe the situation that a second-degree polynomial regression equation would be used to model?
A parabola
If a sample of n = 30 people is selected and the sample correlation between two variables is r = 0.468, what is the test statistic value for testing whether the true population correlation coefficient is equal to zero?
About t = 2.80
(Yachts) Based on this output, which of the independent variables appear to be significantly helping to predict the price of a yacht, using a 0.10 level of significance?
Age and length
The following multiple regression output was generated from a study in which two independent variables are included. The first independent variable (X1) is a quantitative variable measured on a continuous scale. The second variable (X2) is qualitative coded 0 if Yes, 1 if No. Based on this information, which of the following statements is true?
All of the above are true.
(National automotive magazine) Based on this output and your understanding of multiple regression analysis, what is the value of the standard error of the estimate for this model?
Approximately 2.02
The following regression output is available. Notice that some of the values are missing. Given this information, what percent of the variation in the y variable is explained by the independent variable?
Approximately 57 percent
(Yachts) Given this information, what percentage of variation in the dependent variable is explained by the regression model?
Approximately 68 percent
(National automotive magazine) Based on this output and your understanding of multiple regression analysis, what percentage of variation in the dependent variable is explained by the regression model?
Approximately 82 percent
(National automotive magazine) Based on this output and your understanding of multiple regression analysis, what is the critical value for testing the significance of the overall regression model at a 0.05 level of statistical significance?
Approximately F = 2.50
An industry study was recently conducted in which the sample correlation between units sold and marketing expenses was 0.57. The sample size for the study included 15 companies. Based on the sample results, test to determine whether there is a significant positive correlation between these two variables. Use an alpha = 0.05
Because t = 2.50 > 1.7709, reject the null hypothesis. There is sufficient evidence to conclude there is a positive linear relationship between sales units and marketing expense for companies in this industry.
Second-order polynomial models:
Can curve upward or downward depending on the data.
(National automotive magazine) If only one variable were to be brought into the model, which variable should it be if the goal is to explain the highest possible percentage of variation in the dependent variable?
Curb weight
A correlation of -0.9 indicates a weak linear relationship between the variables.
False
A research study has stated that the taxes paid by individuals is correlated at a .78 value with the age of the individual. Given this, the scatter plot would show points that would fall on straight line on a slope equal to .78.
False
You are given the following sample data for two variables: Y X 10 100 8 110 12 90 15 200 16 150 10 100 10 80 8 90 12 150 Based upon these sample data, and testing at the 0.05 level of significance, the critical value for testing whether the population correlation coefficient is equal to zero is t = 2.2622.
False
A perfect correlation between two variables will always produce a correlation coefficient of +1.0
False.
Both a scatter plot and the correlation coefficient can distinguish between a curvilinear and a linear relationship.
False.
If two variables are highly correlated, it not only means that they are linearly related, it also means that a change in one variable will cause a change in the other variable.
False.
If two variables are spuriously correlated, it means that the correlation coefficient between them is near zero.
False.
In a study of 30 customers' utility bills in which the monthly bill was the dependent variable and the number of square feet in the house is the independent variable, the resulting regression model is = 23.40 + 0.4x. Based on this model, the expected utility bill for a customer with a home with 2,300 square feet is approximately $92.00.
False.
In developing a scatter plot, the decision maker has the option of connecting the points or not.
False.
The difference between a scatter plot and a scatter diagram is that the scatter plot has the independent variable on the x-axis while the independent variable is on the Y-axis in a scatter diagram.
False.
The following regression model has been computed based on a sample of twenty observations: = 34.2 + 19.3x. The first observations in the sample for y and x were 300 and 18, respectively. Given this, the residual value for the first observation is approximately 81.6.
False.
Two variables have a correlation coefficient that is very close to zero. This means that there is no relationship between the two variables.
False.
When a correlation is found between a pair of variables, this always means that there is a direct cause and effect relationship between the variables.
False.
ou are given the following sample data for two variables: Y X 10 100 8 110 12 90 15 200 16 150 10 100 10 80 8 90 12 150 The regression model based on these sample data explains approximately 75 percent of the variation in the dependent variable.
False.
(National automotive magazine) Which of the following might explain why no other independent variables entered the model?
Given the two variables already in the model, none of the others could add significantly to the percentage of variation in the y variable that would be explained by the model.
(Yachts) Given this information, what is the null hypothesis for testing the overall model?
H0 : β1 = β2 = β3 = β4 = 0
(National automotive magazine) Based on this output and your understanding of multiple regression analysis, what is the adjusted R-square value for this model?
None of the above
A regression equation that predicts the price of homes in thousands of dollars is t = 24.6 + 0.055x1 - 3.6x2, where x2 is a dummy variable that represents whether the house in on a busy street or not. Here x2 = 1 means the house is on a busy street and x2 = 0 means it is not. Based on this information, which of the following statements is true?
On average, homes that are on busy streets are worth $3600 less than homes that are not on busy streets.
Which of the following is NOT considered to be a stepwise regression technique?
Optimal variable entry and removal regression
Which of the following is a correct interpretation for the regression slope coefficient?
The average change in y of a one-unit change in x will be b1 units.
In a multiple regression, the dependent variable is house value (in '000$) and one of the independent variables is a dummy variable, which is defined as 1 if a house has a garage and 0 if not. The coefficient of the dummy variable is found to be 5.4 but the t-test reveals that it is not significant at the 0.05 level. Which of the following is true?
The house value remains the same with or without a garage.
(Computer magazine) Based on this information, and with a 0.05 level of significance, which of the following conclusions can be justified?
The only significant variable in the model at the .05 level of significance is Hard Drive Capacity.
(Yachts) Given this information, which is correct regarding the test of the overall model using the 0.10 level of significance?
The overall model has significant ability to predict the price of a yacht because p-value = .001 is less than 0.10
(National automotive magazine) Based on this output and your understanding of multiple regression analysis, which of the following statements is true?
The overall multiple regression model explains a significant portion of the variation in highway mileage when tested at a significance level of 0.05.
In a multiple regression model, which of the following is true?
The sum of the residuals computed for the least squares regression equation will be zero.
A decision maker has five potential independent variables with which to build a regression model to explain the variation in the dependent variable. At step 1, variable x3 enters the regression model. Which of the following indicates which of the four remaining independent variables will be next to enter the model?
The variable with the highest coefficient of partial determination
A manufacturing company is interested in predicting the number of defects that will be produced each hour on the assembly line. The managers believe that there is a relationship between the defect rate and the production rate per hour. The managers believe that they can use production rate to predict the number of defects. The following data were collected for 10 randomly selected hours. Given these sample data, the simple linear regression model for predicting the number of defects is approximately = 5.67 + 0.048x.
True
A study was recently performed by the Internal Revenue Service to determine how much tip income waiters and waitresses should make based on the size of the bill at each table. A random sample of bills and resulting tips were collected and the following regression results were observed: Given this output, the point estimate for the average tip per dollar amount of the bill is approximately $0.21.
True
In multiple regression analysis, the model will be developed with one dependent variable and two or more independent variables.
True
The following regression model has been computed based on a sample of twenty observations: = 34.2 + 19.3x. Given this model, the predicted value for y when x = 40 is 806.2.
True
The multiple coefficient of determination measures the percentage of variation in the dependent variable that is explained by the independent variables in the model.
True
The scatter plot is a two dimensional graph that is used to graphically represent the relationship between two variables.
True
A dependent variable is the variable that we wish to predict or explain in a regression model.
True.
A study was recently done in which the following regression output was generated using Excel. Given this output, we would reject the null hypothesis that the population regression slope coefficient is equal to zero at the alpha = 0.05 level.
True.
A study was recently done in which the following regression output was generated using Excel. Given this, we know that approximately 57 percent of the variation in the y variable is explained by the x variable.
True.
A study was recently performed by the Internal Revenue Service to determine how much tip income waiters and waitresses should make based on the size of the bill at each table. A random sample of bills and resulting tips were collected and the following regression results were observed: Given this output, the upper limit for the 95 percent confidence interval estimate for the true regression slope coefficient is approximately 0.28.
True.
If a set of data contains no values of x that are equal to zero, then the regression coefficient, b0, has no particular meaning.
True.
If it is known that a simple linear regression model explains 56 percent of the variation in the dependent variable and that the slope on the regression equation is negative, then we also know that the correlation between x and y is approximately -0.75.
True.
If the correlation between two variables is known to be statistically significant at the 0.05 level, then the regression slope coefficient will also be significant at the 0.05 level.
True.
In a university statistics course a correlation of -0.8 was found between numbers of classes missed and course grade. This means that the fewer classes students missed, the higher the grade.
True.
State University recently randomly sampled ten students and analyzed grade point average (GPA) and number of hours worked off-campus per week. The following data were observed: The correlation between these two variables is approximately -.461
True.
When constructing a scatter plot, the dependent variable is placed on the vertical axis and the independent variable is placed on the horizontal axis.
True.
You are given the following sample data for two variables: Y X 10 100 8 110 12 90 15 200 16 150 10 100 10 80 8 90 12 150 The sample correlation coefficient for these data is approximately r = 0.755.
True.
Under what circumstances does the variance inflation factor signal that multicollinearity may be a problem?
When the VIF is greater than or equal to 5
(Yachts) Which of the following statements is correct using the 0.10 level of significance?
Whether or not the yacht has a flying bridge does not significantly affect the price of a yacht, given the other variables present.
Assume that a time-series plot takes the form of that shown in the following graph: Given this plot, which of the following models would likely give the best fit?
y = b0+ b1t + b1t2+ b1t3