Correlation is a term frequently used in conjunction with regression analysis and is measured by the value of the coefficient of correlation, r. The best explanation of the value r is that it:
Answer(s): D
The coefficient of correlation (r) measures the strength of the linear relationship between the dependent and independent variables. The magnitude of r is independent of the scales of measurement of x and y. The coefficient has a range of-1 to +1. A value of zero indicates no linear relationship between the x and y variables. A value of+1 indicates a perfectly direct relationship, and a value of --1 indicates a perfectly inverse relationship.
In preparing the annual profit plan for the coming year.Based upon the data derived from the regression analysis, 420 maintenance hours in a month would mean the maintenance costs (rounded to the nearest US dollar) would be budgeted at:
Substituting the given data into the regression equation results in a budgeted cost of US $3,746 (rounded to the nearest US dollar).y = a + bx= 684.65 + 7.2884(420)= US $3,746
In preparing the annual profit plan for the coming year.What is the percentage of the total variance that can be explained by the regression equation?
Answer(s): A
The coefficient of determination (r2) measures the percentage of the total variance in cost that can be explained by the regression equation. If the coefficient of determination is .99724, 99.724% of the variance is explained by the regression equation. Thus, the values in the regression equation explain virtually the entire amount of total cost.
The internal auditor of a bank has developed a multiple regression model that has been used for a number of years to estimate the amount of interest income from commercial loans. During the current year, the auditor applies the model and discovers that the r2 value has decreased dramatically, but the model otherwise seems to be working.Which of the following conclusions is justified by the change?
Answer(s): C
The coefficient of determination (r2) is the amount of variation in the dependent variable (interest income) that is explained by the independent variables. In this case, less of the change in interest income is explained by the model. Thus, some other factor must be causing interest income to change. This change merits audit investigation.
What does the following scatter gram suggest?
Internal auditors may use scatter diagrams to detect misstated data, relationships among variables, and unusual operating results. A scatter diagram is a graph of data points.When the points have a systematic relationship, the independent (x) variable and dependent (y) variable are likely to be correlated; i.e.. the value of one variable is a predictor of the value of the other. However, the variables in this scatter gram are clearly uncorrelated because training costs do not predict sales.
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