please answer a~d based on the charts v1_age What is your age? v5_schlevel Wht i

Question

please answer a~d based on the charts

v1_age What is your age? v5_schlevel Wht is the highest level of schooling you intend to complete? 1 Bachelors' degree 2 Professional Masters (MBA, MFA, MEng, JD) 3 Medical Degree (MD and others) 4 Phd Do you think that everyone in this country has an opportunity to obtain an education corresponding to their abilities and talents? v23_eduopp 0 No 1 Yes Some people think America should promote equal opportunity for all, that is, allowing everyone to compete for jobs and wealth on a fair and even basis. Other people think America should promote equal outcomes, that is, insuring that everyone has a decent standard of living and that there are only small differences in wealth and income between the top and bottom in society. Which do you favor: promoting equal v24 equality opportunity or promoting equal outcomes? 1 2 Promote equal opportunity Promote equal outcomes v11hrswork How many hours per week do you work for pay on average during the school year?

Explanation / Answer

NOTE (BEFORE ACTUAL FULL SOLUTION)

equal_opp is new variable generated by recoding v24_equality

= 0 => Promote equal outcomes

=1 => Promote equal opportunities

SOLUTION

Part a.

Response variable: How much they work for, per week, during the school year (v11_hrswrk)

Explanatory variable: Attitude towards educational opportunity (v23) and Attitude towards equality (v24)

Part b. (Let us denote v11_hrswrk by v11 ONLY)

v11 = constant + C1*v23 + C2*v24; C1 and C2 are coefficients determined by multivariate linear regression analysis - the results of which are given in the question. According to this given data,

v11 = 15.4585 + 0.2071792*v23 + (-5.118617)*equal_opp

As noted at the starting, equal opp is a derivative of v24; if v24 = 2, equal_opp = 0. If v24 = 1, equal_opp = 1

i) If there's a change of attitude from 'No' to 'Yes' on eduction_opportunity, there's a change of +0.2071792 work hours on average.

ii) If there's a change of attitude from 'promote equal outcomes' to 'promote equal opportunity' on equality, there's a change of -5.118617 work hours on average.

Part c.

v23 = 'No' = 0 and v_24 = 'promote equal outcomes' = 2 (0 for recoded variable as noted in the beginning)

=> 15.4585 + 0.2071792*0 + (-5.118617)*0 = 15.4585 hours of work on average (Answer c)

Part d.

Significance levels - if p-value for an estimated value is < 0.05 (less than), then the null hypothesis can be rejected (Null hypothesis - the value estimated is actually zero) If we can reject this Null hypothesis, we can say that the estimated value shown in the result of the multiple regression analysis can be considered and is significant. Correspondingly, if the p-value is greater than 0.05, the confidence interval will be too large for the estimated value.

Changes possible:-

1. V23: If the attitude changes from 'No' to 'Yes', the change in hours of work is: 0.207192 (and vice versa). But, this is insignificant as p-value is much higher than 0.05 and hence, confidence interval for the estimated value is too large.

2. V24: If the attitude changes from 'promote equal outcomes' to 'promote equal opportunity', there's a negative change of 5.118617 in the number of hours of work (and vice versa). This is significant as p-value is lower than 0.05 and hence, confidence interval for the estimated value is also relatively acceptable.

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