Question

Use technology to find the regression line to predict \(Y\) from \(X\). $$\begin{array}{llllll} \hline X & 3 & 5 & 2 & 7 & 6 \\\Y & 1 & 2 & 1.5 & 3 & 2.5 \\ \hline\end{array}$$

Short answer

The regression line is given by the equation \(Y = aX + b\), where \(a\) is the slope, and \(b\) is the y-intercept. The exact values will depend on the specific technology used to calculate them.

Step-by-step solution

Input the Data

Typically, scientific calculators and statistical software packages have a data input interface. Using this interface, input the \(X\) and \(Y\) values respectively. For \(X\), the values are 3, 5, 2, 7, 6. For \(Y\), the values are 1, 2, 1.5, 3, 2.5.

Compute Regression Parameters

After inputting the data, the next step is to use the regression analysis function of the calculator or software. This function computes the slope and y-intercept of the regression line. For most devices and software, the output will come in the form of \(Y = aX + b\), where \(a\) is the slope and \(b\) is the y-intercept.

Interpret the Regression Line

Once the calculator or software has computed the values of \(a\) and \(b\), it presents the linear regression equation. The \(a\) (slope) represents the predicted change in \(Y\) for a one-unit change in \(X\), and \(b\) (y-intercept) depicts the predicted value of \(Y\) when \(X\) equals to 0.