Question 5·SAT Desmos Regression Practice·Problem Solving and Data Analysis

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The scatterplot shows the relationship between two variables, $x$ and $y$ .

Which choice is the equation of a line of best fit for the data in the scatterplot?

A line of best fit describes the overall straight trend in a scatterplot, not a rule every dot must follow. Read the direction first, then enter all the plotted pairs in a Desmos table and run a linear regression. Match the fitted slope and intercept to the choices. An unusually low dot can shift the fit, but it shouldn't define the whole trend.

Hints

Hint 1
A positive association means the dots tend to rise as $x$ increases. Look at the main group rather than judging by the low dot at $x=6$ . Should the fitted line rise or fall from left to right?
Hint 2
A regression fits a line to paired observations. Put each dot's horizontal coordinate in $x_1$ and its vertical coordinate in $y_1$ . There are two observations at $x=6$ , so keep both rows.
Hint 3
In $y=mx+b$ , the slope $m$ tells you how much $y$ changes per unit of $x$ . The intercept $b$ is the predicted $y$ at $x=0$ . Match both fitted values to a choice.

Step-by-step

Fit all the plotted points
Step 1
Read the overall direction
Most dots rise from left to right, so the fitted line needs a positive slope. The dot at $(6,12)$ is an outlier, a point far below the main pattern. It doesn't turn the overall trend downward.
Step 2
Keep every plotted pair
Enter the dots in a Desmos table, with $x$ in $x_1$ and $y$ in $y_1$ . The table shows two separate rows for $(6,22)$ and $(6,12)$ . Keep both: the lower dot is still part of the data.
Step 3
Find the fitted slope and intercept
Below the table, type $y_1\sim mx_1+b$ . The $\sim$ tells Desmos to run a linear regression: it chooses a line for all the points, rather than forcing the line through one dot. Under PARAMETERS, Desmos reports $m\approx2.41$ for the slope and $b\approx4.75$ for the predicted $y$ at $x=0$ .
Step 4
Match both parts of the line
In $y=mx+b$ , the fitted slope $2.41$ is closest to $3$ , and the fitted intercept $4.75$ is closest to $4$ . The estimates needn't equal the whole-number coefficients exactly because the dots don't all lie on one line. So $y=4+3x$ is the best choice for the scatterplot. Fit the whole pattern, not one dot. Choice A.

Question 5·SAT Desmos Regression Practice·Problem Solving and Data Analysis

Strategy

Hints

Step-by-step

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Strategy

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