Q.1 The Conference Board produces a Consumer Confidence Index (CCI) that reflects people’s feelings about general business conditions, employment opportunities, and their own income prospects. Some researchers feel that consumer confidence is a function of median household income. Shown here are CCIs for 9 years and median household incomes for the same 9 years published by the U. S. Bureau of the Census. CCCI Income ($1000) a) Determine the equation of the regression line 8 37.415 used to predict the CCI from the median household 68.3 35.015 income 90.5 36.770 62.6 35.237 65.9 34.710 91.6 35.122 125.3 37.010 100.0 35.887 103.7 36.106 b) What is the value of b1? Interpret its meaning in this problem c) Conduct an appropriate test to decide whether median household income is a good predictor of CCI. Use the following ANOVA table: Source of Variability SS df MS F Regression 2872.32 1 2872.32 17.32 Error 1160.89 7 165.84 Total 4033.21 8
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.
Q.1 The Conference Board produces a Consumer Confidence Index (CCI) that reflects people’s feelings about general business conditions, employment opportunities, and their own income prospects. Some researchers feel that consumer confidence is a
CCCI Income ($1000)
a) Determine the equation of the regression line 8 37.415
used to predict the CCI from the median household 68.3 35.015
income 90.5 36.770
62.6 35.237
65.9 34.710
91.6 35.122
125.3 37.010
100.0 35.887
103.7 36.106
b) What is the value of b1? Interpret its meaning in this problem
c) Conduct an appropriate test to decide whether median household income is a good predictor of CCI. Use the following ANOVA table:
Source of Variability SS df MS F
Regression 2872.32 1 2872.32 17.32
Error 1160.89 7 165.84
Total 4033.21 8
d) Use the ANOVA table to determine the coefficient of determination. Explain its meaning in this example. What is the value of the
e) If the median income for the next year is $35,000, what would be the predicted CCI?
f) Find a 95% prediction interval for the CCI in a year in which the median household income is $35,000.
(g) Find a 95% confidence interval for the average CCI for years in which the median household income is $35,000.
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