Question

1. Load the regression data in the le called wagedata.csv and answer the following questions:
(a) Create an interaction between Ability and PhD
(b) Run a regression with the interaction a constant Ability and PhD. Write down you estimators
and the t-statistics
(c) Compute the di erence-in-di erence estimate and write down you answer.
(d) Test if the di erence is signi cant by showing relevant steps, and write down the conclusion to
the test.
2. Which of these photos shows evidence of heteroskedasticity?
0 20 40 60 80 100 120
0 100 200 300 400 500 600
x1
y1
−6 −4 −2 0 2 4 6
−10 0 10 20 30
x
y
−6 −4 −2 0 2 4 6
−10 −5 0 5 10
x
y
−6 −4 −2 0 2 4 6
−10 −5 0 5 10 15
x
y
3. Load the dataset called ec122a.csv and decide the appropriate regression to run. Write down what
transformations, corrections, etc... you make and why.

Data

Wage;"Ability";"Phd"
30	2148858244105;-10	0874543747999;1
21	2139481124597;-0	590192820738451;1
0	804274100356348;18	2611120427467;1
21	2841837231414;-1	56022339054444;1
19	9701441966751;-0	270217314022561;1
-19	3505986647068;15	2847691646256;1
-37	5318232168738;26	0961104031439;1
-27	5104548523827;7	5761567533525;1
1	12580739232134;-1	18594902993318;1
8	46653345914067;0	0785472499891622;1
-4	3851186614386;12	1320105514616;1
3	50685341593623;7	34914917101494;1
-13	9237294518445;18	4776393201793;1
8	19952131952363;3	24253596299393;1
2	061035907599;-0	483248819158479;1
7	77793037392366;5	98655277801752;1
-6	30291122168363;19	5012071181202;1
9	8638921608847;17	2307860456577;1
-1	60927411206267;0	627619361224518;1
18	2636750628683;9	55865292554422;1
-19	85280408247;32	3061680317419;1
-38	3633350768018;27	9436433893924;1
-40	7205010397063;31	6850695595438;1
-56	2602894197782;35	0681431228772;1
-32	9991761971437;27	6280924263471;1
9	7479459402353;7	57174198307181;0
3	92900982953838;0	861977409866384;0
50	248108939599;33	5000136378381;0
30	7461400746423;25	8930976678625;0
49	9814106320709;46	0773964388559;0
37	9566059786407;22	4655728587151;0
68	6497575622049;49	1421665303397;0
61	0701238471535;32	6494107219151;0
55	7189943229771;34	2491817925178;0
51	109332042575;48	4620545148998;0
56	0861713803033;56	2611865964331;0
40	516170174837;29	6930159318191;0
44	0586166449751;35	2492085855466;0
59	6616305513546;45	3875176058839;0
30	4331767384442;38	1275770320187;0
54	8625391374503;41	2616692882961;0
23	5581065455008;42	2396991920984;0
51	6104307198847;49	4530276941521;0
68	8499222925911;57	375001650011;0
34	9282337106992;33	7966475747671;0
59	6531629794339;32	9891986645948;0
48	8530160146515;42	5814753560819;0
41	8592579309319;38	2969055544136;0
68	7653893378851;59	1407240737376;0
57	2611898080186;55	2997953033722;0
71	4317975269271;59	8575740860399;0
84	3041078190792;56	9187686247403;0
86	8127563905414;57	8447954875125;0
53	8947609338275;42	9180372026626;0
75	451187082937;66	4714537888208;0
71	8524802636783;66	5647387578261;0
72	7015631893814;63	9321052241629;0
68	5345645066989;46	9435171993065;0
57	4027012602536;40	8696600009591;0
94	3208057977659;70	4812637532467;0
73	3865424233984;56	9041537923933;0
88	8183392221799;70	0278010012836;0
73	3087112512961;56	9953148483697;0
86	3886013131513;60	5180523355662;0
67	2021941169906;51	0590708916793;0
118	375388309556;94	4572602759228;0
60	6789396907979;61	1500381246522;0
98	719626489431;77	9170774341119;0
71	443350318515;66	314958140777;0
64	6034850016771;58	4809681916044;0
73	1618976038289;65	1237350851343;0
60	4746000022732;63	0423330904353;0
120	289733522426;93	5416148319245;0
107	032173927375;79	1334457282595;0
91	8986502218894;74	6191805319747;0
80	7706797354782;69	0717782611234;0
94	9972106243549;76	4438198039696;0
69	4704718368837;66	2502018108482;0
100	848924827906;80	8871627341593;0
126	836422964446;84	3088129083253;0
123	570430325546;96	9617142388936;0
64	9631783153722;69	8731666565007;0
94	8537176555163;83	4972763448062;0
130	547827259813;91	5406501517776;0
93	4716274384042;79	6440870678146;0
103	69870631698;79	8560598931133;0
90	4185801410255;76	4545817393735;0
87	0684258802465;84	5415174865785;0
145	840161057534;111	032359346546;0
123	719439438811;98	0032391174047;0
117	321770358635;90	845864156288;0
124	037150698884;105	148580858475;0
114	982603027777;94	3143209557192;0
139	514587413482;113	254090704761;0
109	802729838307;91	8569567410886;0
111	534270833463;94	1269472639582;0
99	5545891547564;78	9229661614192;0
95	841141946642;85	3461049648653;0
113	258297584026;96	8252063828309;0
124	340999773273;99	8886185674963;0

Answer 1

Answer:

BY using,given data

(a) By using the scatter plot we can identify the relation between the Ability and Phd.

From the above plot, we can say that if the ability of students increases then the chances of he pursued PhD is decreased.

i.e. Negative correlation in ability and PhD.

(B) The Dependent variable in this data is PhD and

Independent variable in wages and Ability

Dependent variable PhD is not continuous it in categorical form

so ,we used the logistic regression model here,

Model = glm(Phd~Ability+Wage)

Summary.glm(Model)

glm(formula = Phd ~ Ability + Wage)

Coefficients: Estimate Std. Error t value Pr(>|t|)   

(Intercept) 0.799626 0.048791 16.389 < 2e-16 ***
Ability 0.004379 0.002086 2.099 0.0384 *  
Wage -0.011972 0.001347 - 8.886 3.41e-14 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

The coefficient of wage = - 0.011972

The Coefficient of Ability = 0.004379

Test Hypothesis:

H0: The variable is insignificant.

against,

H1: The variable is significant.

Test Statistic:

T-statistic is usefull

t-value of Ability = 2.099

t-value of wage = -8.886

Decision Rule: If p-value is greater than 0.05 level of significance then ,we accept the null hypothesis.
From the above results, p-values are less than 0.05.
we reject the null hypothesis here.

i.e. both are variable significant.

i.e. both variable wage and Ability are important in model.