Question

A regression equation is set up, where the dependent variable is total costs and the independent variable is production. A correlation coefficient of 0.70 implies that:

A. The coefficient of determination is negative
B. The level of production explains 49% of the variation in total costs
C. There is a slightly inverse relationship between production and total costs
D. A correlation coefficient of 1.30 would produce a regression line with better fit to the data

Answer 1

A correlation coefficient of 0.70 indicates a strong positive linear relationship between production and total costs. The coefficient of determination, r², is 0.49, which means that the level of production explains 49% of the variation in total costs.

Step-by-step explanation:

The correlation coefficient, r, measures the strength of the linear association between x and y. A correlation coefficient of 0.70 implies that there is a strong positive linear relationship between the independent variable (production) and the dependent variable (total costs). The closer the value of r is to 1 (positive or negative), the stronger the relationship. In this case, since r = 0.70, it indicates a strong positive relationship between production and total costs.

The coefficient of determination, r², is equal to the square of the correlation coefficient. When expressed as a percentage, r² represents the percentage of variation in the dependent variable, total costs, that can be explained by variation in the independent variable, production, using the regression line. For this question, the correlation coefficient of 0.70 implies that the coefficient of determination, r², is 0.70² = 0.49. This means that the level of production explains 49% of the variation in total costs.