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The equation of the regression line has an R^2 = 95%, and the following regressed equation: Debt...

Question:

The equation of the regression line has an R^2 = 95%, and the following regressed equation: Debt per Capita = -2, 010,000 + 1, 020 middot Year Explain the meaning of the R^2 in this context. For the year 2000, what is the predicted level of Debt per capita? Show and calculate. For the year 2000, what is the residual of Debt per capita, assuming the actual level of Debt per capita is $30,000? Show and calculate. Is the estimate in question 15 an over-estimation or under-estimation of the actual debt per capita? Explain.

Prediction using Linear Regression Model:


A linear regression model is expressed as:

{eq}y = \beta_0 + \beta_1 x {/eq}


{eq}R^2: {/eq} Coefficient of Determination


{eq}R^2 {/eq} is the proportion of the variance in the dependent variable {eq}(y) {/eq} that is explained by the linear relationship between {eq}x {/eq} and {eq}y {/eq}.


{eq}\text {total variation = explained variation + unexplained variation} \\ \sum (y - \bar y)^2 = \sum (\hat y - \bar y)^2 + \sum (y - \hat y)^2 {/eq}

{eq}R^2 =\dfrac {\text{explained variation}}{\text {total variation}} {/eq}


Answer and Explanation:

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The equation of the regression line has an {eq}R^2 = 95% {/eq}, and the following regressed equation: {eq}\text {Debt per Capita} = -2, 010,000 +...

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Simple Linear Regression: Definition, Formula & Examples

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Chapter 8 / Lesson 2
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Simple linear regression is a great way to make observations and interpret data. In this lesson, you will learn to find the regression line of a set of data using a ruler and a graphing calculator.


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