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Question 2 (15 marks in total] University students are expected to attend all classes within a...

Question 2 (15 marks in total] University students are expected to attend all classes within a course. But university adminisTable 1: Q2 Stata output . *===Read data================ . use unitravel . Sumn Obs Mean Std. Dev. Min 723 oo 723 Variable 1= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = · *===Set 3======================= · gen trti

Question 2 (15 marks in total] University students are expected to attend all classes within a course. But university administrators and teaching staff are aware that student attendance can be adversely impacted by a variety of factors including travel time. Also, when attendance rates drop, there are often concerns expressed that it is students most at risk of performing poorly who are not attending class. To better understand some of these issues, a sample of undergraduate students was drawn from a large first year class at a Sydney university. The main outcome of interest is the number of tutorials attended during the first semester course (tut1). Information was also collected on the student's age (age), a dummy variable for gender =1 if female (sex), usual travel time to university in minutes (trtime), their Australian Tertiary Entrance Rank (ATAR) and the usual weekly hours of study during year 12 of high school (yr12hrs). The sample to be considered for analysis excludes any student without an ATAR. Table 1 provides Stata output including summary statistics for the data and three sets (Set 1-Set 3) of regression results. Set1 provides OLS results for a simple regression model for tutorial attendance: (1) tut1 = Bo + B2 trtime + u. (i) Use the Set 1 results to interpret the estimates you obtain for Bo and Bz. Is the sign of the Bzestimate as you expected? Explain. [3 marks) Results for an extended model given by (2) are provided as Set 2. Interpret the new estimate you obtain for B1 and compare it to the estimate you found using model (1). What do you conclude? [3 marks) (2) tut1 = Be + Bztrtime + B2ATAR + Bzyr12hrs + B4age + B5sex+u. (iii) Test Ho:B3 = 0 against an alternative of your choice which you need to justify. Conduct the test and use this as part of a full interpretation of the estimate and the impact of yr12hrs on tutorial attendance. [3 marks] Use the model to predict tutorial attendance for a student who is an 18-year-old male, who usually travels 60 minutes to university, has an ATAR of 95 and usually spent 17 hours a week studying during year 12 of high school. Would you predict that this student would have satisfied the university requirement to attend at least 80% (more than 9 of 11) of tutorials. (Hint: Set 3 results will be useful here.) [4 marks] How well do you consider model (2) explains tutorial attendance? [2 marks] (v
Table 1: Q2 Stata output . *===Read data================ . use unitravel . Sumn Obs Mean Std. Dev. Min 723 oo 723 Variable 1 ----------- --- -- sex tuti 1 age 1 trtime yr12hrs 1 --- ---- ---- outcome ATARI 723 723 723 .473029 9.295989 18.29184 50.08575 17.48409 .4996177 1.775744 1.129694 26.30996 10.91992 1 ONE TW ONI OOOPPix 723 1.594744 87.07878 723 .6905175 6.694015 - 70.1 10.1 99.9 · *===Set 1========== • reg tuti trtime Source SS df MS ----- --- --- -- --- ----- Model 45.005354 1 45.005354 Residual 2231.65301 721 3.09521916 ----------- --------------------------------- - Total | 2276.65837 Number of obs F(1, 721) Prob > F R-squared Adj R-squared Root MSE 723 14.54 0.0001 0.0198 0.0184 1.7593 Std. Err. t P>ti [95% Conf. Interval] - - - - tutil Coef. ----- ------ rtime .0094895 _cons 8.8207 .0024886 .1407735 3.81 62.66 0.000 0.000 .0046037 8.544325 .0143753 9.097075 . *===Set 2=E EEEE=========================================================== • reg tuti trtime ATAR yr12hrs age sex SS Source df MS -- -------- ------- -------------------- ------- Model | 180.682428 5 36.1364856 Residual 2095.97594 717 2.92325794 Number of obs F(5, 717) Prob > F R-squared Adj R-squared Root MSE 723 12.36 0.0000 0.0794 0.0729 1.7098 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Total ! 2276.65837 722 3.15326644 ---------------------- Std. Err. t P>It (95% Conf. Interval] tuti Coef. ---- - ----- trtime .0079578 ATARI .018 9033 yr12hrs | .0067829 age -.3402859 sex . 1185516 cons 13.30113 .002459 .0095883 .0059111 .0570295 . 1301187 1.394257 3.24 1.97 1.15 -5.97 0.91 9.54 0.001 0.049 0.252 0.000 0.363 0.000 .0031301 .0000788 -.0048223 -.4522507 -.1369076 10.56381 .0127855 .0377277 .0183881 -. 2283211 .3740108 16.03844
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = · *===Set 3======================= · gen trtime 60=trtime-60 . gen ATAR95=ATAR-95 • gen yr12hrs 17=yr12hrs-17 · gen age18=age-18 • reg tuti trtime 60 ATAR 95 yri2hrs17 age 18 sex df MS - Source | SS ------------ -- ------- Model | 180.682428 Residual 2095.97594 ----- ------- --- Total 1 2276.65837 5 36.1364856 717 2.92325794 717 , ---- 7 22 3.15326644 Number of obs F(5, 717) Prob > F R-squared Adj R-squared Root MSE 723 12.36 0.0000 0.0794 0.0729 1.7098 - ---- ------- ----- tuti Coef. Std. Err. t P>It! (95% Conf. Interval] ----- --- -- --- -- trtime 60 .0079578 .002459 3.24 0.001 .0031301 0127855 ATAR951 .0189033 .0095883 1.97 0.049 .0000788 .0377277 yr12hrs17 .0067829 .0059111 1.15 0.252 -.0048223 .0183881 age18 -. 3402859 .0570295 -5.97 0.000 -.4522507 -.2283211 sex .1185516 .1301187 0.91 0.363 -.1369076 .3740108 cons 9.564569 .1236186 77.37 0.000 9.321871 9.807266 --- ------ ------ ------- ------ ----- ------------------------ ------- ------ ------ -
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Answer #1

(i) tut(1) = B0 +B1 trtime + u

tut(1) = 8.8207 +0.0094 trtime + u----- (From Set 1)

where trtime stands for usual travel time for university in minutes.The B0 coefficient implies that if the Travel time is zero a student attends approximately 8 Tutorials.  The coefficient of trtime from set 1 i.e the value of B1 = 0.0094.This implies that as Travel time increases by 1 minutes the Number of Tutorials increases by 0.0094. The sign of B1 according to this particular study is positive which is contradicting my belief. I believe that as the time taken to Reach the university increases , the number of Tutorials attended should fall. Thus according to me the sign of B1 has to be negative.

(ii) tut(1) = B0+ B1trtime + B2 ATAR+ B3yr12hrs + B4 age +B5sex + u

tut(1) = 13.301 +0.07958 trtime + 0.0189 ATAR+0.067829 yr12hrs-0.3402 age + 0.11855 sex + u

After including other variables in the model the B1 coefficient in set 2 is 0.0795 while the value of B1 in set 1 is 0.0094 . When other variables were included the value of B1 falls . Thus when other variables like age sex and hours are included in the model a 1 minute increase in travel time increases the number of tutorial attended by 0.07.

(iii)Ho B3-0 H, 3 t0 7 cal Rejection arva Rejec on Ragyon Se -196 I 14716 O o6782 9 O O. 05911 1145 At 5/ lend igi al to et the Nu

(v) The R squared value from the Set 3 is 0.0794 which implies that only 7 % of the change in Number of Tutorial attended depends on Usual Travel time, Australian Tertiary Entrance Rank, weekly hours of study during year 12 of high school , age and sex. Thus model 2 does not satisfactorily explain changes occurring Number of Tutorial attended.

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