Linear Models

[mathdad]

The following data represent the weight (in grams) of a box of raisins and the number of raisins in the box.

Weight (in grams) w

42.3
42.3
42.8
42.4
42.6

Number of Raisins R

87
87
93
87
89

Note: The variables w and R represent a point in the form ( w, R).

A. Draw a scatter diagram of the data treating weight as the independent variable.

I understand this to mean to plot points on the wR-plane. Is this correct?

B. Select two points and find a linear model that contains the points.

My Approach:

1. Pick two points.
2. Find the slope m.
3. Plug one of the points and the slope m into the point-slope formula.
4. Solve for y.

C. Use the linear model to predict the number of raisins in a box that weighs 42.3 grams.

I am not too sure about part C.

 

[Dr.Peterson]

What equation did you get?

For part c, just plug x = 42.3 into that equation and find y. The idea is that if all points (not just the two you picked) were on the line, then the equation would give the value of y for each of them.

 

[Harry_the_cat]

The following data represent the weight (in grams) of a box of raisins and the number of raisins in the box.

Weight (in grams) w

42.3
42.3
42.8
42.4
42.6

Number of Raisins R

87
87
93
87
89

Note: The variables w and R represent a point in the form ( w, R).

A. Draw a scatter diagram of the data treating weight as the independent variable.

I understand this to mean to plot points on the wR-plane. Is this correct? Yes.


B. Select two points and find a linear model that contains the points.

My Approach:

1. Pick two points.
2. Find the slope m.
3. Plug one of the points and the slope m into the point-slope formula.
4. Solve for y. Solve for c.
You will end up with a linear equation in the form y=mx+c or actually R = mw + c. (Sometimes b is used instead of c, doesn't really matter)

C. Use the linear model to predict the number of raisins in a box that weighs 42.3 grams.
Once you have the equation from B, plug in w = 42.3 and calculate R.

I am not too sure about part C.

 

[mathdad]

What equation did you get?

For part c, just plug x = 42.3 into that equation and find y. The idea is that if all points (not just the two you picked) were on the line, then the equation would give the value of y for each of them.

I made a typo. The value of R that corresponds with the value for w 42.4 is 90 not 87. Anyway, the equation I got is
R = 30w - 1356. You said for part C, simply let x = 42.3 and do the math. I can take it from here. Note: Let x = w since we are talking about the wR-plane.

 

[mathdad]

I got it. Thank you.