Hi, I'm not sure if I'm giving the correct answer for this problem. The question states; The values of computers in the years after its purchase date are listed in the following table. Year 0=1500, Year1=1200, Year2=1100,Year3 +1000, Year 4 = 800, Year 5 =400, Year 6= 200. Givent hat the equation of the regression line between value and year is y = -207.14x + 1507.14 with an R^2 value of 0.9622, how reliable do you think the regression equation is at predicting the future value of a computer in 5 years?
My answer: first I drew a scatter plot, then I got the correlation coefficient which is 0.981. I preidicted strong, negative correlation. I'm just concerned this isn't the correct procedure because the next question asks me to calculate the corrrelation coefficient between year and value which I already did for this question. Any help is greatly appreciated.
(5,400)
the actual value of y-the predicted value
400-471.44=-71.44 big difference between the actual value and predicted value of y therefore the regression equation is not very reliable.
To determine the reliability of the regression equation at predicting the future value of a computer in 5 years, you need to evaluate the coefficient of determination (R^2 value) and its interpretation.
The coefficient of determination (R^2) measures the proportion of the variation in the dependent variable (value) that can be explained by the independent variable (year) in the regression equation. It ranges from 0 to 1, where 0 indicates no relationship between the variables, and 1 indicates a perfect predictive relationship.
In this case, the given R^2 value is 0.9622, which is close to 1. This indicates that 96.22% of the variation in the values of computers can be explained by the year variable in the regression equation.
Based on this interpretation, it can be concluded that the regression equation is highly reliable at predicting the future value of a computer in 5 years. This high R^2 value suggests a strong predictive relationship between the year and the value of computers.
Regarding your concern about calculating the correlation coefficient between year and value, you have correctly calculated it to be 0.981. The correlation coefficient measures the strength and direction of the linear relationship between the two variables. It helps in assessing the level of linear association but is less informative about the predictive power of a regression equation in terms of future values.
In summary, you followed the correct procedure by calculating the correlation coefficient (0.981) and correctly interpreting it as a strong negative correlation. Additionally, the high R^2 value (0.9622) demonstrates the reliability of the regression equation in predicting the future value of a computer in 5 years.