21. 600,000 students in 79 countries take a PISA test every three years to evaluate their learning in reading, math, and science. Students in the Beijing-ShanghaiJiangsu-Zhejiang regions in China scored the highest average scores in all three subjects in 2018. Canada ranked around 12 overall but has had steadily declining scores in math and science. We have data on average math scores and characteristics of 500 school districts across Canada. This problem asks you to build up a regression model to look for factors that affect average math test scores in various school districts in Canada.

I run a basic regression equation that explains math scores (SCORE) as a function

of:

1. STR = the student teacher ratio. (number of students per teacher)

2. SPEND = government spending per student in the school district in dollars per student.

3. HIESL= a dummy variable=1 if the percentage of students learning English as a new language is above 20% and = if it is below 20%. The regression also includes the usual constant term.

There is a categorical variable called PROVINCE for the province of the school district. This variable =1 for Ontario, =2 for Quebec, =3 for Alberta, and =4 for British Columbia.

There is also a categorical variable called INCOME which is the average per capita income of households in the school district. INCOME = 1 if the district has average per capital income below $40000, E2 if the district has per capita income between $40000 and $60000, =3 if the district has per capita income >= $60000.

How do I add PROVINCE and INCOME into my regression model? Which specification is correct?

A. SCORE = b +62 STR + b3SPEND + b&HIESL + DSPROVINCE + DEINCOME

where PROVINCE takes values 1 to 4

and INCOME takes values 1 to 3.

B. SCORE = 1 +b2STR + b3SPEND + b&HIESL + b5ON + b5QC + b&BC +b7INC2 + b3INC3

where

ON = 1 if the district is in Ontario and otherwise

QC = 1 if the district is in Quebec and 0 otherwise

BC = 1 if the district is in BC and 0 otherwise

INC2 = 1 if the district is the middle income range and otherwise

INC3 = 1 if the district is the high income range and 0 otherwise

C. SCORE = 1 +b2STR + b3SPEND + 4HIESL + b5ON + b&QC +b7BC + b3AB +b7INC2 + b3INC3

where

ON = 1 if the district is in Ontario and 0 otherwise

QC = 1 if the district is in Quebec and 0 otherwise

BC = 1 if the district is in BC and otherwise

AB = 1 if the district is in Alberta and 0 otherwise

INC2 = 1 if the district is the middle income range and 0 otherwise

INC3 = 1 if the district is the high income range and 0 otherwise

D. SCORE = 51 + b2STR + b3SPEND + 4HIESL + b5ON + b6QC +b7BC + b3AB + b3INC1 + b10INC2 + b11INC3

where

ON = 1 if the district is in Ontario and 0 otherwise

QC = 1 if the district is in Quebec and 0 otherwise

BC = 1 if the district is in BC and 0 otherwise

AB = 1 if the district is in Alberta and 0 otherwise

INC1 = 1 if the district is the low income range and 0 otherwise

INC2 = 1 if the district is the middle income range and 0 otherwise

INC3 = 1 if the district is the high income range and 0 otherwise

E. SCORE = b STR + b3SPEND + 4HIESL + b5ON + b&QC+b7BC + bgAB + b3INC1 +10INC2 + b11INC3

where

ON = 1 if the district is in Ontario and otherwise

QC = 1 if the district is in Quebec and 0 otherwise

BC = 1 if the district is in BC and 0 otherwise

AB = 1 if the district is in Alberta and 0 otherwise

INC1 = 1 if the district is the low income range and 0 otherwise

INC2 = 1 if the district is the middle income range and 0 otherwise

INC3 = 1 if the district is the high income range and otherwise