Question

The aim of a logit model was to determine mobile phone ownership as a function of (logarithm of) income. Mobile phone ownership was a binary variable: Y = 1 if a household owns a mobile phone, zero otherwise.

Li = −2.77231 + 0.347582 ln(Income)

t = (−3.35)   (4.05)

χ 2 (1 df) = 16.681 (p value = 0.0000);

where; Li = estimated logit and where ln Income is the logarithm of income. The χ2 measures the

goodness of fit of the model.

Use the information from the regression output to answer the following questions.

Q.6.3 What is the probability that a household with an income of R20,000 will own a mobile phone?

Q.6.4 What are the odds of owning a mobile phone for a household with an income level of

R20,000?

Q.6.5 Comment on the statistical significance of the estimated logit model.

Answer 1

Li = −2.77231 + 0.347582 ln(Income)

Q6.3:

Income = 20000

Hence, Li = −2.77231 + 0.347582 ln(Income)

=−2.77231 + 0.347582 ln(20000)

=0.669964

ln(P/(1-P))=0.669964

P/(1-P) = e^(0.669964)

P = 0.338505

Thus, the probability that a household with an income of R20,000 will own a mobile phone is 33.8505%

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Q6.4

The odds of owning a mobile phone for a household with an income level of R20,000 is given by P/(1-P)

Hence, Li = −2.77231 + 0.347582 ln(Income)

=-2.77231 + 0.347582 ln(20000)

=0.669964

ln(P/(1-P))=0.669964

P/(1-P) = e^(0.669964)

=1.954167

This is 1.954167

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Q6.5

The actual p-value corresponding to the chi-square of 16.681 for the given logit model is 0.0000, which is less than the critical p-value of 0.05, indicating that the given logit model is statistically significant at 5% level of significance.