Age Gender1 PhD1 Age:Gender1 Age:PhD1 Gender1:PhD1 1 47 1 1 47 47 1 2 65 0 1 0 65 0 3 56 0 0 0 0 0 4 23 1 0 23 0 0 5 53 0 1 0 53 0 6 27 0 0 0 0 0 lasso second_order (Intercept) 0.6552865 3.11406026 Age 0.7224603 0.05061385 Gender1 0.0000000 -1.36231149 PhD1 28.2808951 4.50344953 Age:Gender1 0.1513879 0.03158918 Age:PhD1 0.0000000 -0.04378838 Gender1:PhD1 13.4895940 0.83154192 [1] 0.7042244 7 x 1 sparse Matrix of class "dgCMatrix" s1 (Intercept) 1.1797542 Age 0.7159047 Gender1 . PhD1 28.0061605 Age:Gender1 0.1470606 Age:PhD1 . Gender1:PhD1 13.4759045

using the above data give answer for below question.

- Assuming that age is fixed, the expected gap in college teacher salary between a female with a PhD and a female without a PhD is \$1.69 thousand.

- Still assuming that age is fixed, the expected gap in salary between a male with PhD and a male without a PhD is \$(1.69 + .28) thousand or approximately \$2 thousand.

- For each additional year of age, we expect that college teacher salary will increase on average by $30 with gender and PhD status held constant.

There is a **major** error that is common to all three of these interpretation sentences. Explain what is incorrect about all of these statements.