BUS Analytics Chapter 3 and 4

In the graph of the simple linear regression equation, the parameter β1 is the _____ of the regression line. a. slope b. x-intercept c. y-intercept d. end-point

A. In the graph of the simple linear regression equation, the parameter β1 is the slope of the regression line.

What would be the coefficient of determination if the total sum of squares (SST) is 23.29 and the sum of squares due to regression (SSR) is 10.03? a. 2.32 b. 0.43 c. 13.26 d. 0.89

B. The coefficient of determination r2 = SSR/SST. Substituting the given values we get r2 =0.43.

Tables should be used when a. the reader need not refer to specific numerical values. b. the reader need not make precise comparisons between different values and not just relative comparisons. c. the values being displayed have different units or very different magnitudes. d. the reader need not differentiate the columns and rows.

C. The tables should be used when the reader needs to refer to specific numerical values, when the reader needs to make precise comparisons between different values and not just relative comparisons, and when the values being displayed have different units or very different magnitudes.

What would be the value of the sum of squares due to regression (SSR) if the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89? a. 31.89 b. 19.32 c. 18.43 d. 15.32

C. The three quantities are related as SST = SSR + SSE. Substituting the values, we get SSR=18.43.

When the mean value of the dependent variable is independent of variation in the independent variable, the slope of the regression line is _____. a. positive b. zero c. negative d. infinite

When the mean value of the dependent variable is independent of the variation in the independent variable, the slope of the regression line is zero.

A two-dimensional graph representing the data using different shades of color to indicate magnitude is called a ______. a. heat map b. bubble chart c. column chart d. pie chart

A. A heat map is a two-dimensional graphical representation of data that uses different shades of color to indicate magnitude. Heat maps depend strongly on the use of color to convey information over different areas, across time, or both.

A linear regression analysis for which any one unit change in the independent variable is assumed to: a. have the same change in the dependent variable. b. have no change in the dependent variable. c. have an inverse effect on the dependent variable d. have a nullifying effect on the dependent variable.

A. A regression analysis for which any one unit change in the independent variable is assumed to result in the same change in the dependent variable is referred to as a linear regression.

_____ is used to test the hypothesis that the values of the regression parameters β1, β2, . . . , βq are all zero. a. An F test b. A t test c. The least squares method d. Extrapolation

A. An F test is used to test the hypothesis that the values of the regression parameters β1, β2, . . . , βq are all zero.

Which of the following inferences can be drawn from the scatter chart given below? a. The residuals have a varying variance. b. The model captures the relationship between the variables accurately. c. The regression model follows the F probability distribution. d. The residual distribution is consistently scattered about zero.

A. The variation in the residuals e increases as the value of the independent variable x increases, suggesting that the residuals do not have a constant variance.

Consider the clustered bar chart of the dashboard developed to monitor the performance of a call center: This chart allows the IT manager to a. identify a particular type of problem by the call volume. b. identify a particular type of problem by location. c. identify different types of problems (Email, Internet, or Software) in the call center. d. identify the frequency of each problem in the call center.

B. The clustered bar chart shows the call volume in the call center by type of problem (Email, Internet, or Software) for each of three cities in Texas. This chart allows the IT manager to quickly identify if there is a particular type of problem by location.

The following scatter chart would help conclude that: a. the residuals have a constant variance. b. the model fails to capture the relationship between the variables accurately. c. the model underpredicts the value of the dependent variable for intermediate values of the independent variable. d. the residual is normally distributed.

B. The residuals are positive for small and large values of the independent variable x but are negative for the remaining values of the independent variable. This pattern suggests that the linear relationships in the regression model underpredicts the value of dependent variable for small and large values of the independent variable and overpredicts the value of the dependent variable for intermediate values of the independent variable. In this case, the regression model does not adequately capture the relationship between the independent variable x and the dependent variable y.

In order to visualize three variables in two-dimensional graph, we use a a. 2-D chart. b. 3-D chart. c. bubble chart. d. column chart.

C. A bubble chart is a graphical means of visualizing three variables in a two-dimensional graph and is therefore, sometimes a preferred alternative to a 3-D graph.

A useful type of table for describing data of two variables is a a. data table. b. bubble chart. c. crosstabulation. d. scatter chart.

C. A crosstabulation provides a tabular summary of data for two variables.

A regression analysis involving one independent variable and one dependent variable is referred to as a_____. a. factor analysis b. time series analysis c. simple regression d. data mining

C. A regression analysis involving one independent variable and one dependent variable is referred to as a simple regression.

Data-ink is the ink used in a table or chart that a. does not help in conveying the data to the audience. b. helps in presenting data when the audience need not know exact values. c. is necessary to convey the meaning of the data to the audience. d. increases the Non-data-ink ratio.

C. Data-ink is the ink used in a table or chart that is necessary to convey the meaning of the data to the audience

If the scatter chart indicates a positive linear relationship between two variables, then their correlation coefficient is a. equal to -1. b. greater than 1. c. between 0 and +1. d. between -1 and 0.

C. If the scatter chart indicates a positive linear relationship between two variables, then their covariance is positive and hence, their correlation coefficient is between 0 and +1.

The procedure of using sample data to find the estimated regression equation is better known as _____. a. point estimation b. interval estimation c. the least squares method d. extrapolation

C. The least squares method is a procedure for using sample data to find the estimated regression equation.

A _____ is a line that provides an approximation of the relationship between the variables. a. line chart b. sparkline c. trendline d. gridline

C. To obtain an approximate relationship between the variables, we add a trendline on a scatter chart.

A _____ is a graphical presentation of the relationship between two quantitative variables. a. histogram b. bar chart c. pie chart d. scatter chart

D. A scatter chart is a graphical presentation of the relationship between two quantitative variables.

A line chart displaying the data values collected over a period of time is termed as a a. boxplot. b. frequency graph. c. dot plot d. time series plot.

D. Line charts are very useful for time series data collected over a period of time (minutes, hours, days, years, etc.). Such line charts are often called as time series plots.

Prediction of the value of the dependent variable outside the experimental region is called _____. a. interpolation b. forecasting c. averaging d. extrapolation

D. Prediction of the value of the dependent variable outside the experimental region is called extrapolation.

The coefficient of determination: a. takes values between -1 to +1. b. is equal to zero for a perfect fit. c. is equal to one for the poorest fit. d. is used to evaluate the goodness of fit.

D. The coefficient of determination (R-squared) is used to evaluate the goodness of fit for the estimated regression equation

Which of the following inferences can be drawn from the scatter chart given below? a. The residuals have a constant variance. b. The model captures the relationship between the variables accurately. c. The model underpredicts the value of the dependent variable for intermediate values of the independent variable. d. The residual distribution is not normally distributed.

D. The residuals in the given figure are not symmetrically distributed around zero; many of the negative residuals are relatively close to zero, while the relatively few positive residuals tend to be far from zero. This skewness suggests that the residuals are not normally distributed.