$\newcommand{\E}{\mathbb{E}}$

For this problem, we will use the Caschools data which you can load with the following command (you may need to install the Ecdat package first if you have not previously done so)

data(Caschool, package="Ecdat")

I would like for you to run a regression of mathscr on the following variables: grspan, enrltot, teachers, calwpct, mealpct, computer, compstu, expnstu, str, avginc, elpct.

Besides the intercept, which regressor has the largest t-statistics in absolute value, and what is the t-statistic?

Rules:

• No rules!

To win

• Raise your hand, answer the question, and you are the winner

Solution below…

data(Caschool, package="Ecdat")
reg <- lm(mathscr ~ grspan + enrltot + teachers + calwpct + mealpct + computer + compstu + expnstu + str + avginc + elpct, data=Caschool)
summary(reg)
##
## Call:
## lm(formula = mathscr ~ grspan + enrltot + teachers + calwpct +
##     mealpct + computer + compstu + expnstu + str + avginc + elpct,
##     data = Caschool)
##
## Residuals:
##      Min       1Q   Median       3Q      Max
## -30.9365  -6.6218  -0.1643   5.4444  30.2329
##
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept)  6.694e+02  1.158e+01  57.814  < 2e-16 ***
## grspanKK-08 -4.200e+00  1.425e+00  -2.946 0.003402 **
## enrltot      4.245e-05  1.928e-03   0.022 0.982447
## teachers    -9.168e-03  4.259e-02  -0.215 0.829675
## calwpct     -1.335e-01  6.829e-02  -1.955 0.051304 .
## mealpct     -3.151e-01  4.291e-02  -7.345 1.13e-12 ***
## computer     4.373e-03  3.663e-03   1.194 0.233268
## compstu      8.566e+00  9.087e+00   0.943 0.346407
## expnstu     -9.255e-05  1.065e-03  -0.087 0.930762
## str         -2.882e-01  3.814e-01  -0.756 0.450193
## avginc       6.948e-01  1.049e-01   6.624 1.11e-10 ***
## elpct       -1.591e-01  4.154e-02  -3.830 0.000148 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.839 on 408 degrees of freedom
## Multiple R-squared:  0.732,  Adjusted R-squared:  0.7247
## F-statistic: 101.3 on 11 and 408 DF,  p-value: < 2.2e-16

The largest t-statistic (in absolute value) is for mealpct and it is equal to -7.345.