Building a Multiple Linear Regression Model With LEGO Brick Data

Figures & data

Table 1 Summary statistics.

Variable	Theme	Mean	S.D.	Minimum	Maximum
Number of pieces	City	274.64	231.95	37	897
	Friends	280.12	213.10	37	722
	Duplo	34.60	30.53	6	129
Amazon price	City	45.27	34.56	8.99	149.99
	Friends	38.65	35.28	7.99	184.99
	Duplo	34.26	30.26	6.29	128.95

Fig. 1 Scatterplot displaying the relationship between the Amazon price and the number of pieces.

Fig. 2 Scatterplot displaying the relationship between the Amazon price and the number of pieces for LEGO City and LEGO Friends sets.

Fig. 3 Multiple linear regressions prediction expression output for additive model.

Fig. 4 Scatterplot displaying the relationship between the Amazon price and the number of pieces for small and large brick sets.

Fig. 5 Multiple linear regressions prediction expression output for model with interaction.

Table 2 Example responses from a virtual implementation of the activity.

Topics in activity	Actual student group responses
Describing the difference in y-intercepts of parallel lines	“The difference tells us that there is a predicted difference in cost between the two sets of $6.04. The prices increase with the number of pieces at an equal rate for both sets, but a Lego City set costs $6.04 more than an equivalent Lego Friends set.”
Describing the coefficient of the Theme variable in the additive model	“The coefficient in front of Theme 2 indicated the difference in y-intercepts. This makes the equation conditional to distinguish between the predicted price of Lego City versus Lego Friends.”
	“We think that it could tell us how much of an effect the Theme has on the price. Essentially, it represents the price increase when going from a LEGO Friends set to a City set.”
Describing the purpose of the coefficient of the Size variable in the interaction model	“The size 2 slope shows us how much of an effect the size of the pieces has on the amazon price of the lego set, depending on if the indicator variable is added to the prediction equation.”
	“The purpose of the slope for Size 2 allows us to change the y-intercept. For large pieces, this y-intercept will change because the slope value is being added. However, for small pieces, the y-intercept will not change because the slope value is being multiplied by zero, and therefore, it cancels out in the equation.”
Describing the purpose of the coefficient of the interaction	“The slope of (Pieces)(Size 2) is the same as the increase in slope between small pieces and large pieces per piece, which is 0.59. The predicted price goes up by 59 cents per piece from small piece sets to large piece sets.”