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 $h_{ii}=0.37$ , then it is an indication to trace the leverage point in the regression model.

(iv) In a regression model $Y=\beta _0+\beta_1X_1+\beta_2X_2+\varepsilon ,$ 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 $\left [ -log(1-\pi) \right ].$

02 Apr 2024

Answer :

Word Count : 303

(i) True. In regression models, when an explanatory variable has more than two categories, we typically create (k-1) indicator variables for a variable with k categories to avoid the dummy variable trap. For an explanatory variable with three categories, two indicator variables are required.

(ii) False. The adjusted R-squared is a modified version of the coefficient of determination (R-squared) that _____ ____ ______ _________ ___ ____ _____ ___ ____.
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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

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

Employee	Test 1	Test 2	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	79	64	96
15	50	85	71	65	75	76