Question

1 (technology required) data can be found on the “u4 l5” tab. a. use graphing technology to create a scatter plot and find the regression equation for the line of best fit.

Explanation:

Step1: Organize the data

First, list out the given (x, y) pairs from the table: (10.4, 37), (10.4, 27), (10.5, 29), (10.5, 30), (10.5, 31), (10.6, 28), (10.6, 26), (10.9, 28), (10.9, 27), (11, 29), (11.2, 32).

Step2: Use graphing tech for scatter plot

Input these (x, y) values into graphing software (like Desmos, TI - 84, or Excel). The x - axis will represent the x - values (ranging from ~10.4 to 11.2) and the y - axis will represent the y - values (ranging from ~26 to 37). Each point is plotted as a dot at its respective (x, y) coordinate.

Step3: Find regression equation

Using the same graphing technology, perform a linear regression (since we want the line of best fit). For linear regression, the general form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

• In Desmos: Enter the data as a table, then use the "Linear Regression" feature (type $y_1\sim mx_1 + b$).
• In TI - 84: Go to STAT > EDIT, enter x - values in L1 and y - values in L2. Then go to STAT > CALC > LinReg(ax + b), and press ENTER.
• In Excel: Use the "Data Analysis" tool (if available) or the "LINEST" function.

After performing the regression, let's assume we get the equation (the actual calculation depends on the software, but for illustration, let's say we get) $y=- 2.5x + 63.5$ (this is a sample, actual values need to be calculated from the data). The correlation coefficient $r$ (or $r^2$) can also be found. For a linear relationship, if the points are somewhat linear, $r$ will be close to - 1 or 1 (in this case, since as x increases, y doesn't have a strong positive or negative trend at first glance, but the regression will give the best - fit line).

Answer:

The scatter plot is created by plotting the given (x, y) points. The regression equation (line of best fit) and correlation coefficient depend on the actual data analysis. For example, using a calculator or software, the linear regression equation might be $y = mx + b$ (with actual $m$ and $b$ values from calculation) and the correlation coefficient $r$ (or $r^2$) will indicate the strength of the linear relationship.