Question

y = 505.51x - 995806

r² = 0.9964

Find and state the value of r², the coefficient of determination, and r, the correlation coefficient. Discuss your findings in a few sentences. Is r positive or negative? Why? Is a line a good curve to fit to this data? Why or why not? Is the linear relationship very strong, moderately strong, weak, or nonexistent?

Choose a value of interest and use the line of best fit to make an estimate or prediction. Show calculation work.

Write a brief narrative of a paragraph or two. Summarize your findings and be sure to mention any aspect of the linear model project (topic, data, scatterplot, line, r, or estimate, etc.) that you found particularly important or interesting.

Answer 1

Given Linear equation is

Y(hat)= 505.51*X-995806

R squared=0.9964

The value of coefficient of determination R squared = 0.9964. 0.9964 indicates that the model explains 99.64% of the variability of the response data around its mean.

Correlation Coefficient is square root of coefficient of determination.

r= sqrt(0.9964)

r= 0.9982

r is POSITIVE .Because the slope of the equation is POSITIVE.

Yes , line is a good curve to fit to this data because of high R squared value.

The linear relationship very strong because r =0.9982 is close to 1.

Suppose X= 2000 Units

Y(hat)= 505.51*X-995806

Y(hat)= 505.51*420-995806

Y(hat)= 15214 Units

For X=2000 Units the predicted Value= 15214 Units.