4.44 The Consumer Behavior Report is designed to provide insight into online shopping trends.9 A recent report asked the question, “In the past three months, how has the current state of the economy impacted your money spending on online purchasing?’’ Here are the results from 3156 online consumers: Reduced spending Gender No Yes Female 586 708 Male 1074 788 (a) What proportion of individuals plan to reduce their spending in each gender? (b) What is the odds ratio for comparing female individuals to male individuals? (c) Write the logistic regression model for this problem using the log odds of reducing spending as the response variable and an indicator of gender as the explanatory variable.
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
14.44 The Consumer Behavior Report is designed to provide insight into online shopping trends.9 A recent report asked the question, “In the past three months, how has the current state of the economy impacted your money spending on online purchasing?’’ Here are the results from 3156 online consumers:
| Reduced spending | ||
| Gender | No | Yes |
| Female | 586 | 708 |
| Male | 1074 | 788 |
(a) What proportion of individuals plan to reduce their spending in each gender?
(b) What is the odds ratio for comparing female individuals to male individuals?
(c) Write the logistic regression model for this problem using the log odds of reducing spending as the response variable and an indicator of gender as the explanatory variable.
(d) Software gives the estimated slope b1 5 0.4988 and its standard error SEb1 5 0.0729. Transform this result to the odds scale and compare it with your answer in part (b).
(e) Construct a 95% confidence interval for the odds ratio and write a short conclusion.
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