Say you have a regression where you are regressing wages on several variables, one being Years of Education (X1). In this regression, you estimate βˆx1 = 1.5 and it is statistically significant. Suppose you then find there is information of individuals SAT scores (an approximate measure of underlying ability) and add it to your regression as X2. You now get that βˆx1 = 0.5 and is still statistically significant, and you get βˆx2 = 0.1 and it is also statistically significant. What type of relationship to you suspect there is between Years of Education, SAT scored, and wages? Touch on the correlation of each variable to every other variable and explain the likely causal pathways. If cor(x1, y) ≡ 0.5, and cor(x2, y) ≡ 0.5, explain when regressing y on x1 and x2 gives an R2 of 0.5
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Say you have a regression where you are regressing wages on several variables, one being Years of Education (X1). In this regression, you estimate βˆx1 = 1.5 and it is statistically significant. Suppose you then find there is information of individuals SAT scores (an approximate measure of underlying ability) and add it to your regression as X2. You now get that βˆx1 = 0.5 and is still statistically significant, and you get βˆx2 = 0.1 and it is also statistically significant. What type of relationship to you suspect there is between Years of Education, SAT scored, and wages? Touch on the
correlation of each variable to every other variable and explain the likely causal pathways. -
If cor(x1, y) ≡ 0.5, and cor(x2, y) ≡ 0.5, explain when regressing y on x1 and x2 gives an R2 of 0.5
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