The following problem is reprinted from the November 1989...

The following problem is reprinted from the November 1989 Actuarial Examination on Applied Statistical Methods. Source: Society of Actuaries. You are given $$\begin{array}{|c|cccc|}\hline {X} & {6.8} & {7.0} & {7.1} & {7.2} & {7.4} \\ \hline{Y} & {0.8} & {1.2} & {0.9} & {0.9} & {1.5}\\ \hline\end{array}$$ Determine $r^{2},$ the coefficient of determination for the regression of $Y$ on $X .$ Choose one of the following. (Note: The coefficient of determination is defined as the square of the correlation coefficient.) a. $0.3 \qquad$ b. $0.4 \qquad$ c. $0.5 \qquad$ d. $0.6 \qquad$ e. $0.7$

The following problem is reprinted from the November 1989 Actuarial Examination on Applied Statistical Methods. Source: Society of Actuaries.
You are given
$$\begin{array}{|c|cccc|}\hline {X} & {6.8} & {7.0} & {7.1} & {7.2} & {7.4} \\ \hline{Y} & {0.8} & {1.2} & {0.9} & {0.9} & {1.5}\\ \hline\end{array}$$
Determine $r^{2},$ the coefficient of determination for the regression of $Y$ on $X .$ Choose one of the following. (Note: The coefficient of determination is defined as the square of the correlation coefficient.)
a. $0.3 \qquad$ b. $0.4 \qquad$ c. $0.5 \qquad$ d. $0.6 \qquad$ e. $0.7$

Key Concepts

Simple Linear Regression

Simple linear regression involves modeling a linear relationship between two variables by fitting a straight line through the data points. In this model, one variable is considered the predictor (independent variable) while the other is the response (dependent variable). The method uses the least squares approach to minimize the sum of the squared differences between observed and predicted values.

Correlation Coefficient

The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where values near 1 or -1 indicate a strong linear relationship, and values near 0 indicate a weak linear relationship. Squaring this coefficient gives the coefficient of determination.

Coefficient of Determination

The coefficient of determination quantifies the proportion of variability in a dependent variable that is explained by the linear relationship with an independent variable. It is computed as the square of the correlation coefficient, offering a measure of how well data points fit a statistical model, particularly in regression analysis.

Transcript

Please give Ace some feedback