State whether the following statements are true or false and also give

Question

State whether the following statements are true or false and also give the reason in support of your answer.

(i) We define three indicator variables for an explanatory variable with three categories.

(ii) If the coefficient of determination is 0.833, the number of observations and explanatory variables are 12 and 3, respectively, then the Adjusted R² will be 0.84.

(iii) For a simple regression model fitted on 15 observations, if we have h₁ = 0.37, then it is an indication to trace the leverage point in the regression model.

(iv) In a regression model $Y=\beta_0+\beta_1 X_1+\beta_2 X_2+\varepsilon,\text{if}H_0:\beta_1=0$ is not rejected, then the variable X₁ will remain in the model.

(v) The logit link function is log [-log(1-π)].

29 Apr 2025

Answer :

Word Count : 264

(i) False
Reason: For an explanatory variable with three categories, we define two indicator (dummy) variables, not three. The number of indicator variables is always one less than the number of categories to avoid multicollinearity (the dummy variable trap).

(ii) False
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Employee	Test 1	Test 1	Test 3	Test 4	Test 5	IQ
1	83	80	78	77	67	99
2	73	85	67	80	63	92
3	81	80	71	81	68	94
4	96	86	82	83	56	99
5	84	73	75	75	68	94
6	72	74	71	67	59	79
7	84	79	84	84	69	97
8	54	86	61	69	53	92
9	86	85	79	78	76	94
10	42	71	60	80	56	86
11	83	72	72	78	74	98
12	63	86	65	85	56	83
13	69	76	64	85	61	98
14	81	84	65	85	64	96

S. No	. Cholesterol (mg/dL)	SBP (mm/Hg)
1	300	150
2	410	270
3	380	210
4	530	310
5	570	350
6	490	310
7	340	210
8	320	150
9	280	110
10	550	320
11	340	220
12	350	170
13	410	260
14	390	230
15	450	270

S. No.	Serum Cholesterol (mg/dl)	Weight (kg)	Number of Patients having CHD	Total Number of Patients
1	420	60	10	20
2	450	68	15	30
3	400	54	4	15
4	510	74	2	10
5	480	62	1	5