Question #1
The coefficient of determination (R-squared) shows the proportion of variance in the dependent variable, which is explained by the independent variable. Let’s say, the independent variable is the amount of money invested by a population of investors and the dependent variable is their profits received. Assume, the R-squared between the variables is 0.8567. This means that approximately 85.67% of the variance of profit received is explained by the amount of invested money.
Question #2
This phrase means that if the coefficient of correlation shows a strong relationship between the variables, it not always mean that there is a real causal relationship between these two factors. It is a possible to get a high correlation coefficient for an individual’s height and number of words he reads per minute. Obviously, there is no causation between the factors. However, the high correlation can be explained by the third factor – age. We know that kids read slower than adults, and the adults are usually taller. That’s why the correlation coefficient can be high, and we get the “illusion” of a misleading conclusion: “taller people read faster”.
Question #3
Use the regression equation given on the graph:
y60=-0.1341*60+12.88=4.834
The oxygen solubility at 60 degrees is 4.834 mg/L.
Question #4
The high value of the coefficient of determination (0.95486) shows that the relationship is very close to linear, because the linear model fits the data good enough. The strength of the relationship is calculated from the r-squared value:
r=R2=0.9772
This is the evidence of a very strong positive linear association between the variables.
