Question 38·SAT Desmos Regression Practice·Problem Solving and Data Analysis

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A botanist measured the height $h$ (in centimeters) of a vine after $w$ weeks of growth. The data are shown in the scatterplot.

Which choice is the most appropriate linear model for the relationship between $h$ and $w$ ?

A linear model describes a straight trend using a slope, the height gained per week, and an intercept, the height at week $0$ . For measured points on a scatterplot, a Desmos table and linear regression can estimate both numbers. Compare both with the choices: a line can have the right growth rate but the wrong starting height.

Hints

Hint 1
Each dot pairs an input with an output. Put weeks in $x_1$ and the height measured at that week in $y_1$ . Keep the two coordinates of each dot in the same table row.
Hint 2
A linear regression fits a straight line to all the points. Type $y_1\sim mx_1+b$ after entering the table; the $\sim$ tells Desmos to find values for $m$ and $b$ .
Hint 3
In $h=mw+b$ , the slope $m$ is centimeters gained per week, while $b$ is the height at week $0$ . Which choice matches both fitted values?

Step-by-step

Fit the plotted points in Desmos
Step 1
Pair each week with its measured height
Read the axes first: weeks are the input, and height is the output. Enter the plotted dots as approximate pairs in a Desmos table, with weeks in $x_1$ and heights in $y_1$ . For example, the leftmost dot is about $(0,3.1)$ and the rightmost is about $(6,15.1)$ . Desmos shows each week's height beside that week.
Step 2
Fit a line to the measurements
Type $y_1\sim mx_1+b$ . The regression fits a line to the overall trend instead of requiring every measured dot to lie on it. Under PARAMETERS, Desmos shows $m\approx2.01$ and $b\approx3.07$ . So the fitted line gains about $2.01$ centimeters per week and starts at about $3.07$ centimeters.
Step 3
Match both parts of the model
The closest offered slope is $2$ , and the closest starting height is $3$ . Match both the slope and the starting height to the scatterplot. Matching only the slope would miss that a line starting at $6$ centimeters is too high at week $0$ . The vine's height is best modeled by $h=2w+3$ . Choice B.

Question 38·SAT Desmos Regression Practice·Problem Solving and Data Analysis

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