Q1. 807 people were randomly selected and data was collected on whether or not they smoked cigarettes in the past 12 months (smoked = 1 if they did, smoked = 0 otherwise), their years of schooling (educ), the natural log of their annual income in dollars (In[income]), age in years (age), and race (white = 1 if white, white = 0 otherwise). The following logit models were estimated and the results are summarized in the table below. The numbers in parentheses are the standard errors. (1) logit (2) logit (3) sample average constant 1.43 0.02 (0.40) -0.10 (1.06) educ -0.11 12 (0.03) (0.03) In[income] 0.16 10.8 (0.11) -0.02 age -0.02 41 (0.0004) (0.0004) white 0.02 0.7 (0.23) log-likelihood -525 -524 In column (2), the regression equation for smokeď* is: smoked* = x'3 +e= B1 + Bzeduc + 33 In[income]+ B4age + Bzwhite + e In column (3), the sample averages of the regressors are listed. For example, 12 is the sample average of educ, 10.8 is the average of In[income], etc. (a) Using the results in column (1), does the probability of being a smoker depend on one's education level? In other words, is educ a significant variable at the 5% level? In order answer, you must compute the appropriate test statistic, find a critical value, and explain your conclusion. (b) Mr. Smatresk has 20 years of education and is 70 years old. Using the results in column (1), what is the probability that he smoked a cigarette in the past 12 months? (c) Treating age as a continuous variable and using the results in column (1) along with the sample averages, calculate the partial effect of age on the probability of being a smoker. (d) Carry out a joint significant test of In[income] and white at the 1% significance level. In your answer, you must compute the appropriate test statistic, find a critical value, and explain your conclusion.
Q1. 807 people were randomly selected and data was collected on whether or not they smoked cigarettes in the past 12 months (smoked = 1 if they did, smoked = 0 otherwise), their years of schooling (educ), the natural log of their annual income in dollars (In[income]), age in years (age), and race (white = 1 if white, white = 0 otherwise). The following logit models were estimated and the results are summarized in the table below. The numbers in parentheses are the standard errors. (1) logit (2) logit (3) sample average constant 1.43 0.02 (0.40) -0.10 (1.06) educ -0.11 12 (0.03) (0.03) In[income] 0.16 10.8 (0.11) -0.02 age -0.02 41 (0.0004) (0.0004) white 0.02 0.7 (0.23) log-likelihood -525 -524 In column (2), the regression equation for smokeď* is: smoked* = x'3 +e= B1 + Bzeduc + 33 In[income]+ B4age + Bzwhite + e In column (3), the sample averages of the regressors are listed. For example, 12 is the sample average of educ, 10.8 is the average of In[income], etc. (a) Using the results in column (1), does the probability of being a smoker depend on one's education level? In other words, is educ a significant variable at the 5% level? In order answer, you must compute the appropriate test statistic, find a critical value, and explain your conclusion. (b) Mr. Smatresk has 20 years of education and is 70 years old. Using the results in column (1), what is the probability that he smoked a cigarette in the past 12 months? (c) Treating age as a continuous variable and using the results in column (1) along with the sample averages, calculate the partial effect of age on the probability of being a smoker. (d) Carry out a joint significant test of In[income] and white at the 1% significance level. In your answer, you must compute the appropriate test statistic, find a critical value, and explain your conclusion.
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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![Q1. 807 people were randomly selected and data was collected on whether or not they smoked
cigarettes in the past 12 months (smoked = 1 if they did, smoked = 0 otherwise), their years of
schooling (educ), the natural log of their annual income in dollars (In[income]), age in years (age),
and race (white = 1 if white, white = 0 otherwise). The following logit models were estimated and
the results are summarized in the table below. The numbers in parentheses are the standard errors.
(1)
logit
(2)
logit
(3)
sample average
constant
1.43
0.02
(0.40)
(1.06)
educ
-0.10
-0.11
12
(0.03)
(0.03)
In[income]
0.16
10.8
(0.11)
age
-0.02
-0.02
41
(0.0004) | (0.0004)
white
0.02
0.7
(0.23)
log-likelihood
-525
-524
In column (2), the regression equation for smokeď* is:
smoked* = x'3 + e = B1 + B2educ + B3 In[income] + B4age + B5white + e
In column (3), the sample averages of the regressors are listed. For example, 12 is the sample
average of educ, 10.8 is the average of In[income], etc.
(a) Using the results in column (1), does the probability of being a smoker depend on one's
education level? In other words, is educ a significant variable at the 5% level? In order
answer, you must compute the appropriate test statistic, find a critical value, and explain
your conclusion.
(b) Mr. Smatresk has 20 years of education and is 70 years old. Using the results in column (1),
what is the probability that he smoked a cigarette in the past 12 months?
(c) Treating age as a continuous variable and using the results in column (1) along with the
sample averages, calculate the partial effect of age on the probability of being a smoker.
(d) Carry out a joint significant test of In[income] and white at the 1% significance level. In your
answer, you must compute the appropriate test statistic, find a critical value, and explain
your conclusion.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea0084d8-63e7-4f56-975c-add2c9289a98%2Ff48e6b57-6a91-46bc-92b2-8c97bfb460ba%2Fdfchml_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q1. 807 people were randomly selected and data was collected on whether or not they smoked
cigarettes in the past 12 months (smoked = 1 if they did, smoked = 0 otherwise), their years of
schooling (educ), the natural log of their annual income in dollars (In[income]), age in years (age),
and race (white = 1 if white, white = 0 otherwise). The following logit models were estimated and
the results are summarized in the table below. The numbers in parentheses are the standard errors.
(1)
logit
(2)
logit
(3)
sample average
constant
1.43
0.02
(0.40)
(1.06)
educ
-0.10
-0.11
12
(0.03)
(0.03)
In[income]
0.16
10.8
(0.11)
age
-0.02
-0.02
41
(0.0004) | (0.0004)
white
0.02
0.7
(0.23)
log-likelihood
-525
-524
In column (2), the regression equation for smokeď* is:
smoked* = x'3 + e = B1 + B2educ + B3 In[income] + B4age + B5white + e
In column (3), the sample averages of the regressors are listed. For example, 12 is the sample
average of educ, 10.8 is the average of In[income], etc.
(a) Using the results in column (1), does the probability of being a smoker depend on one's
education level? In other words, is educ a significant variable at the 5% level? In order
answer, you must compute the appropriate test statistic, find a critical value, and explain
your conclusion.
(b) Mr. Smatresk has 20 years of education and is 70 years old. Using the results in column (1),
what is the probability that he smoked a cigarette in the past 12 months?
(c) Treating age as a continuous variable and using the results in column (1) along with the
sample averages, calculate the partial effect of age on the probability of being a smoker.
(d) Carry out a joint significant test of In[income] and white at the 1% significance level. In your
answer, you must compute the appropriate test statistic, find a critical value, and explain
your conclusion.
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