Find the regression equation for predicting final score from...

Find the regression equation for predicting final score from midterm score, based on the following information:
$$\begin{array}{cl}{\text { average midterm score }=70,} & {\text { SD }=10} \\ {\text { average final score }=55,} & {\text { SD }=20, \quad r=0.60}\end{array}$$

Key Concepts

Linear Regression

Linear regression is a statistical technique used to model and analyze the relationship between two quantitative variables. It involves fitting a linear equation, typically expressed as y = a + bx, to the observed data so that one can predict the dependent (response) variable based on the independent (predictor) variable.

Correlation Coefficient

The correlation coefficient, denoted as r, measures the strength and direction of the linear relationship between two variables. It provides insight into how well the predictor variable can explain the variation in the response variable, with values closer to 1 or -1 indicating a strong linear relationship.

Slope Calculation

The slope of the regression line indicates the expected change in the dependent variable for each one-unit increase in the independent variable. It is computed by multiplying the correlation coefficient (r) by the ratio of the standard deviation of the dependent variable to the standard deviation of the independent variable.

Intercept Calculation

The intercept of the regression line represents the predicted value of the dependent variable when the independent variable is equal to zero. It is calculated by subtracting the product of the slope and the mean of the independent variable from the mean of the dependent variable.

Standard Deviation

Standard deviation is a measure of the dispersion or spread of data points around the mean. In the context of linear regression, the standard deviations of the dependent and independent variables are used to normalize the slope, thereby adjusting for differences in their scales.

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