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In this vignette we will show how the legosets dataset can be used to teach basic regression. This, of course, can be extended to other modeling techniques. To begin, we will filter the data frame to include sets from the last 10 years and remove any sets with missing values.
data(legosets)
last_year <- max(legosets$year)
legosets <- legosets |>
dplyr::select(year, US_retailPrice, pieces, minifigs, themeGroup) |>
dplyr::filter(year %in% seq(last_year - 10, last_year)) |>
na.omit()Our goal is to predict US_retailPrice from pieces (number of Lego pieces in the set), minifigs (number of mini figures in the set), and themeGroup (the set theme).
First, let’s plot the data to see if there is a relationship between our dependent variable and indepedent variables.
ggplot(legosets, aes(x = pieces, y = US_retailPrice, size = minifigs, color = themeGroup)) +
geom_point(alpha = 0.2)
The contingency table reveals that “Licensed” themes are the largest category. To help with interpreting our results we will convert the themeGroup variable to a factor and ensure that “Licensed” is our reference group.
table(legosets$themeGroup, useNA = 'ifany')
#>
#> Action/Adventure Basic Educational Historical
#> 469 4 6 6
#> Junior Licensed Miscellaneous Model making
#> 52 1375 171 130
#> Modern day Pre-school
#> 742 192legosets$themeGroup <- as.factor(legosets$themeGroup)
legosets$themeGroup <- relevel(legosets$themeGroup, ref = 'Licensed')Now we can run our linear regression.
lm_out <- lm(US_retailPrice ~ pieces + minifigs + themeGroup, data = legosets)
summary(lm_out)
#>
#> Call:
#> lm(formula = US_retailPrice ~ pieces + minifigs + themeGroup,
#> data = legosets)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -210.529 -7.451 -2.163 5.726 256.691
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 7.107e+00 7.103e-01 10.006 < 2e-16 ***
#> pieces 9.074e-02 6.746e-04 134.496 < 2e-16 ***
#> minifigs 1.053e+00 1.630e-01 6.461 1.20e-10 ***
#> themeGroupAction/Adventure -7.913e+00 1.076e+00 -7.353 2.47e-13 ***
#> themeGroupBasic -2.303e+01 1.007e+01 -2.287 0.022254 *
#> themeGroupEducational 2.305e+02 8.270e+00 27.875 < 2e-16 ***
#> themeGroupHistorical -7.890e+00 8.245e+00 -0.957 0.338618
#> themeGroupJunior 1.239e+00 2.849e+00 0.435 0.663728
#> themeGroupMiscellaneous -5.746e+00 1.630e+00 -3.525 0.000429 ***
#> themeGroupModel making -1.552e+01 1.933e+00 -8.032 1.34e-15 ***
#> themeGroupModern day -1.647e-01 9.212e-01 -0.179 0.858149
#> themeGroupPre-school 2.295e+01 1.572e+00 14.601 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 20.1 on 3135 degrees of freedom
#> Multiple R-squared: 0.9186, Adjusted R-squared: 0.9183
#> F-statistic: 3215 on 11 and 3135 DF, p-value: < 2.2e-16The adjusted R-squared for our model is 91.8%.
Finally, we can check that our residuals are normally distributed.
legosets$predicted <- predict(lm_out)
legosets$residuals <- resid(lm_out)
ggplot(legosets, aes(x = residuals)) + geom_histogram(binwidth = 10)
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