Final answer:
The question pertains to the criteria for identifying cost drivers in regression modeling, emphasizing the relationship between independent and dependent variables, construction of scatter plots, calculation of a least-squares regression line, and significance of the correlation coefficient.
Step-by-step explanation:
The question revolves around the identification of cost drivers for a regression model, which requires a clear understanding of the relationship between independent and dependent variables. When analyzing such relationships, certain criteria must be considered to establish a reliable regression model.
Variables Identification
In any given situation, first identifying the independent and dependent variables is crucial. For example, if we are looking at the relationship between power consumption (independent variable) and utility bills (dependent variable), we would use the power consumption to predict the expected utility bills.
Scatter Plot and Regression Line
After identifying the independent and dependent variables, we construct a scatter plot to visualize the data points. Observing the scatter plot can provide an initial understanding of whether there is a potential relationship between the variables. To analyze this relationship further, we calculate the least-squares regression line, often represented as ŷ = a + bx, where 'a' is the y-intercept and 'b' is the slope.
Correlation and Significance
The correlation coefficient, r, measures the strength and direction of the linear relationship between the variables. If r is close to 1 or -1, it indicates a strong positive or negative relationship, respectively. To test the significance of the correlation coefficient, we typically use hypothesis testing, often resulting in a p-value that determines if the correlation is statistically significant.
An additional measure, the coefficient of determination, denoted as r², indicates the proportion of variance in the dependent variable that is predictable from the independent variable.