Answer:
a) See below.
b) $911 billion
c) See below.
Explanation:
Linear regression is a statistical technique used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to the observed data.
It estimates the slope and y-intercept of a straight line that minimizes the overall distance between the observed data points and the predicted values. The linear regression equation is y = ax + b.
Part a
The association between year and amount of disposable income is indicated by the linear regression equation y = ax + b.
The value of a is the slope of the linear regression line, and represents the average rate of change in disposable income per year. As a = 14.0545, it means that the disposable income increases by approximately $14.0545 billion dollars each year.
As the value of r (correlation coefficient) is very close to +1, it indicates a very strong positive linear correlation between the year and disposable income. This suggests that as the years progress, the disposable income tends to increase.
Part b
Linear regression equation:
To predict the amount of disposable income for the year 2000, we can substitute x = 2000 into the linear regression equation:
Therefore, the predicted amount of disposable income for the year 2000 is approximately $911 billion.
Part c
The predicted value of $911 billion for the year 2000 is significantly lower than the actual value of $8128 billion. This implies that the model is not accurately capturing the increasing trend in disposable income over time, leading to an underestimation of the income level in 2000. This suggests that the model may have limitations or inaccuracies when extrapolating beyond the range of the provided data. It indicates the need for caution and further analysis when using the model to make predictions outside of the given timeframe.