Remember that the number of powerboats registered ( \(X\)) was given in thousands. This means that for each one-unit increase in \(X\), we expect a corresponding increase in \(Y\) of 0.129 units. The slope of the regression equation is 0.129. It provides a mathematical relationship between the. If the slope of a line is \(\frac = -42.542 0.129 \cdot Powerboats In simple linear regression, the starting point is the estimated regression equation: b0 b1x. If the slope is negative, the values of \(Y\) decrease as \(X\) increases. When the slope is expressed as a fraction, the numerator tells how much the points on the line change vertically as you move to the right the distance indicated by the denominator. If the slope is positive, then the values of \(Y\) increase as the values of \(X\) increase. It is sometimes described as rise over run. The slope of a line is a measure of how steep the line is. Given the equation of a line, you can find the Y-intercept by substituting \(X = 0\) and solving for \(Y\). Stated differently, the Y-intercept is the value of \(Y\) that corresponds to \(X = 0\). The Y-intercept is the value at which the line crosses the Y-axis. Two important characteristics of a line are its slope and its Y-intercept. A linear equation is the technical term for any equation that describes a line.
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