Question

Introduction: The Chartered Financial Analyst (CFA) designation is the de facto professional certification for the financial industry. Employers encourage their prospective employees to complete the CFA exam. Daniella Campos, an HR manager at Solid Rock Investment, is reviewing 10 job applications. Given the low pass rate for the CFA Level 1 exam, Daniella wants to know whether or not the 10 prospective employees will be able to pass it. Historically, the pass rate is higher for those with work experience and a good college GPA. With this insight, she compiles the information on 100 current employees who took the CFA level 1 exam last year, including the employee’s success on the exam (1 for pass, 0 for fail), the employee’s college GPA, and years of work experience.

1. Estimate a linear probability model to predict the probability of passing the CFA exam as a function of college GPA, and years of work experience.
2. Interpret the regression coefficient for college GPA, and years of work experience.

3. Pass	GPA	Experience
   0	3.62	4
   0	3.64	9
   1	2.89	15
   1	3.56	17
   0	2.95	5
   1	3.67	15
   1	3.87	13
   1	3.01	14
   0	3.99	14
   1	3.2	18
   0	3.61	8
   0	2.6	5
   0	2.87	6
   0	3.99	4
   1	3.83	15
   1	3.48	17
   1	3.9	15
   0	3.17	12
   0	3.8	3
   0	3.5	12
   1	2.54	13
   1	3.84	13
   1	3.22	8
   0	3.08	3
   1	3.11	6
   1	2.91	10
   0	3.53	3
   0	2.95	8
   1	2.63	8
   0	2.53	4
   0	3.39	11
   0	3.13	7
   0	3.39	4
   0	3.79	11
   1	3.47	15
   0	3.82	13
   1	3.09	10
   1	2.97	9
   0	3.54	17
   0	3.24	14
   0	3.11	10
   1	3.61	17
   0	3.36	11
   0	2.89	5
   1	2.7	12
   0	2.55	12
   1	3	16
   1	3.94	17
   0	3.92	8
   1	2.8	12
   0	2.88	15
   0	3.07	6
   0	3.18	2
   1	3.33	9
   0	2.91	4
   1	3.7	17
   0	2.62	3
   1	2.79	18
   1	3.28	10
   1	3.55	7
   0	2.91	13
   1	3.94	11
   0	2.58	12
   0	3.96	8
   1	3.96	15
   0	2.67	9
   0	3.89	5
   1	3.94	11
   1	2.76	8
   0	3.13	3
   0	2.9	6
   0	2.68	6
   1	3.72	16
   0	2.99	6
   0	3.99	14
   1	2.88	8
   0	2.99	12
   1	3.16	17
   0	2.93	3
   1	3.23	6
   1	3.22	11
   0	3.32	4
   0	2.51	7
   0	3.14	16
   1	3.23	17
   0	3.75	12
   1	3.42	4
   0	2.89	11
   0	3.04	7
   0	2.53	5
   1	3.04	8
   1	3.61	15
   0	2.65	11
   1	3.42	13
   0	3.62	5
   1	2.74	11
   0	2.76	3
   1	3.28	18
   0	3.27	10
   1	3.9	2

Answer 1

I have taken all the 100 observations and performed the regression. The regression output is as follows

In the output below, there are only some obsrevations, becuase all of them can't fit in, But i have taken all the observations while doing regression analysis

Question (a)

The linear probability model to predict probability of passing the CFA exam as a function of college GPA, and years of work experience is

Probability of passing the exam = -0.207417 + 0.048401 * GPA + 0.050109 * Experience

If we round the coefficients and intercept value to two decimals the regression equation is

Probability of passing the exam = -0.21 + 0.05 * GPA + 0.05 * Experience

Question (b)

Coefficient for College GPA

The coefficient for College GPA is 0.048401 which is positive implies that the Probablity of passing the exam and College GPA are positively correlated

If the value of College GPA increases, Probablity of passing the exam increases while Work Experience is held constant.

If the value of College GPA decreases, Probablity of passing the exam decreases while Work Experience is held constant.

If college GPA increases by 1, then the probability of passing the exam will increase by 0.048401 while Work Experience is held constant. If college GPA decreases by 1, then the probability of passing the exam will decrease by 0.048401 while Work Experience is held constant.

oefficient for years of Work Experience

The coefficient for year of Work Experience is 0.050109 which is positive implies that the Probablity of passing the exam and Years of work experience are positively correlated

If the value of Years of work experience increases, Probablity of passing the exam increases while College GPA is held constant.

If the value of Years of work experience decreases, Probablity of passing the exam decreases while College GPA is held constant.

If Years of Work Experience increases by 1, then the probability of passing the exam will increase by  0.050109 while College GPA is held constant. If Years of Work Experience decreases by 1, then the probability of passing the exam will decrease by  0.050109 while College GPA is held constant.