Question

Load the regression data in the file 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 difference-in-difference estimate and write down you answer.

(d) Test if the difference is significant by showing relevant steps, and write down the conclusion to the test.

Wage	Ability	Phd
3.52942833628898	2.57892317214096	1
11.5241044105103	0.217444617867018	1
6.43708200805673	-1.87272626133237	1
-3.32998520783711	3.76202232083705	1
5.36855439782834	2.45761717163884	1
4.68954400067837	3.7301993415098	1
1.53267822456788	11.1874554691197	1
9.10512634961242	14.776972741187	1
15.1980826548641	8.04953747508578	1
-0.974975683769769	15.0886996846141	1
-2.27397066450858	14.1018765774721	1
4.07844378728811	18.0404548280347	1
2.91124460624012	16.146272599743	1
0.639521049463678	15.1627671917362	1
3.87999908956868	14.4806487625393	1
0.86624292704353	17.1927478743176	1
1.274343525654	12.2506520697683	1
12.2440679213768	7.03907961805346	1
4.62183553362942	12.3302790116668	1
-5.80284504254266	19.5789275529377	1
-4.30925497568042	24.1056351458815	1
-2.540612755397	33.9056390962157	1
4.61808124007202	27.0868971199435	1
-6.09378187954794	23.4770820717889	1
1.89284719138658	23.6506044409556	1
-3.57578516914426	30.0878257593232	1
-10.4832960381058	27.7379587998238	1
-4.23469650902542	26.0756352330111	1
0.32636023954342	25.3765945327823	1
-2.14382778065676	19.8725582444871	1
-6.49958909150258	35.6254259276013	1
-4.2123776901225	38.4425354882262	1
-9.93866128806339	26.3440031742927	1
-10.8848237411726	39.371788202531	1
-14.5898267483555	41.7790947678189	1
31.9672982079939	28.1874684151412	0
53.0399296766834	40.9782587746505	0
41.9762536303933	36.3474948524008	0
41.4195063143274	35.3147598374969	0
66.3803136922626	46.7735149473553	0
51.020150726321	42.441586812062	0
55.1426542676839	37.1127928048265	0
42.0002523740924	36.2514856675758	0
58.9807345842352	42.0202531433013	0
49.1566524898706	44.1867225082533	0
63.6602309428108	50.8654657866704	0
64.4549685409955	47.1389281386783	0
64.2523581270013	50.5426848501408	0
57.6322627991752	49.8164124706117	0
59.2379083072777	45.4707627503926	0
75.0097119730034	58.6045656879896	0
72.0414413343758	56.9033438179064	0
60.11541218912	46.490135284302	0
82.3487653047187	62.9586420142269	0
71.7931186135558	54.710408977031	0
73.2218390933929	55.4135631594282	0
80.1643459284332	65.0883281938915	0
89.6605408631406	67.0526293063506	0
77.6714308086706	59.1652498150208	0
60.1866041058332	52.6935105007023	0
78.8931332800096	63.853165068676	0
75.6680771247174	65.9387678255181	0
91.350499040367	69.2295415546537	0
79.2193601260624	65.3677494814196	0
82.2098222546892	69.4671573562542	0
76.0164190216985	69.245488783903	0
83.1686288653623	69.5506074646669	0
87.8263238377056	74.064957110444	0
90.5135137636898	74.1568120165115	0
92.5954649559386	73.4822071147249	0
107.674755182245	74.566781189438	0
89.9950131910464	72.2801914267274	0
97.4615796572152	76.6063161465292	0
105.708466642139	76.7970200186916	0
88.7188928120122	72.2666282430883	0
107.460432925572	78.9891028126621	0
100.817186976305	80.7244942614467	0
95.4164293622049	83.2000481949651	0
98.2242952265557	80.5249862903271	0
101.74649150486	81.7876152620241	0
120.114427097958	83.9020330907207	0
105.321989123658	85.2532850888778	0
92.8089874267733	75.5563434470352	0
104.382782310878	80.6783286434761	0
102.334140991132	82.7305998908955	0
113.219858886703	89.4615028214495	0
99.6334461954748	79.9346366347533	0
97.6623079623431	85.2233221804249	0
133.049229396789	98.3074188253643	0
125.524235994978	98.8716498346646	0
110.136953858669	89.7559456979701	0
121.235963787882	97.8541667388593	0
108.441898301419	95.9326418499836	0
125.632137997864	98.3088827726876	0
120.143232384763	97.9600091543673	0
117.697955727987	97.297574476134	0
112.051373301533	89.4706843427284	0
125.352843080085	101.125171811127	0
107.445393968235	93.5846018140228	0
123.668736337728	102.649631689373	0

Answer 1

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 here

t-value of Ability = 2.099

t-value of wage = -8.886

Decision Rule: If p-value 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 variable significant

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