Hi6007 Statistics For Business Decisions-Independent Assessment Answers

Answer:

Consumer Research, Inc., is an independent agency that conducts research on consumer attitudes and behaviours for a variety of firms. In one study, a client asked for an investigation of consumer characteristics that can be used to predict the amount charged by credit card users. Data were collected on annual income, household size, and annual credit card charges for a sample of 50 consumers. The following data are recorded for Consumer information.

Solution

1. Develop estimated regression equations, first using annual income as the in- dependent variable and then using household size as the independent variable. Which variable is the better predictor of annual credit card charges? Discuss your findings.

Solution

1. Regression model using annual income as the in- dependent variable

The above tables give the regression results. From the results we deduce that; the model is fit to predict the amount charged (p-value < 0.05). The value of R-Squared is 0.3979; this shows that only 39.79% of the variation in amount charged on credit card is explained by the income.

The coefficient of income is 40.47; this means that a unit increase in income would result to an increase in the amount charged on credit card by 40.47

The intercept coefficient is 2204.24; this means that holding other factors constant we would expect the amount charged on credit card to be $2204.24.

The regression model is thus;

1. Regression model using household size as the independent variable

The above tables give the regression results. From the results we deduce that; the model is fit to predict the amount charged (p-value < 0.05). The value of R-Squared is 0.5668; this shows that only 56.68% of the variation in amount charged on credit card is explained by the household size.

The coefficient of household size is 404.16; this means that a unit increase in household size would result to an increase in the amount charged on credit card by 404.16.

The intercept coefficient is 2581.64; this means that holding other factors constant we would expect the amount charged on credit card to be $2581.64.

The regression model is thus;

Best model

Regression model using household size as the independent variable is the better predictor of annual credit card charges

1. Develop an estimated regression equation with annual income and household size as the independent variables. Discuss your findings.

Solution

The above tables give the regression results. From the results we deduce that; the model is fit to predict the amount charged (p-value < 0.05). The value of R-Squared is 0.8254; this shows that only 82.54% of the variation in amount charged on credit card is explained by the household size and annual income.

The coefficient of income is 33.12; this means that a unit increase in income would result to an increase in the amount charged on credit card by 33.12.

The coefficient of household income is 356.34; this means that a unit increase in household income would result to an increase in the amount charged on credit card by 356.34.

The intercept coefficient is 1305.03; this means that holding other factors constant we would expect the amount charged on credit card to be $1305.03.

The regression model is thus What is the predicted annual credit card charge for a three-person household with an annual income of $40,000? the need for other independent variables that could be added to the model. What additional variables might be helpful?

Solution

Looking at the performance of the regression equation models, we observed that addition of the variables resulted to a better model. This means that the necessary independent variables need to be added to ensure that the model is towards becoming a perfect one.

1. For each correlation discuss the results:
   • Are they are positive/negatively correlated?
   • Are they weak or strong correlations?
   • What is the significance value?
   • What does the significance value reveal about the data we have used?

Solution

Yes there are both positively and negatively correlated relationships. 23 correlations were positively correlated while 13 correlations were negatively variables.

32 correlations had a weak relationship while 4 correlations had a strong relationship.

Significance value also known as p-value is the probability of getting a result that is equal to or "more extreme" than what was actually observed, given that the null hypothesis is true. 

The significance value reveals that 11 correlations were significant while the remaining 25 correlations were insignificant.

As part of a long-term study of individuals 65 years of age or older, sociologists and physicians at the Wentworth medical Center in upstate New York investigated the relationship between geographic location and depression. A sample of 60 individuals, all in reasonably good health, was selected; 20 individuals were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. Each of the individuals sampled was given a standardized test to measure depression.

The data collected follow; higher test scores indicate higher levels of depression. These data are available on the website that accompanies this text in the file named medical1. A second part of the study considered the relationship between geographic location and depression for individuals 65 years of age or older who had a chronic health condition such as arthritis, hypertension, and/or heart ailment. A sample of 60 individuals with such conditions was identified. Again, 20 were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. The levels of depression recorded for this study follow. These data are available on the website that accompanies this text in the file named medical2.

Required:

1. Use descriptive statistics to summarize the data from the two studies. What are your preliminary observations about the depression scores?

Solution

Preliminary observations indicates that residents from Florida have lower depression scores when compared to the two other states. Residents of New York are the most depressed lot of people.

1. Use analysis of variance on both data sets. State the hypotheses being tested in each case. What are your conclusions?

Solution

We conducted a one-way ANOVA to test whether the mean depression scores are equal across the three states. The hypothesis we sought to test is;

H_o: the mean depression scores are equal across the three states

H₁: at least one of the states has a different mean depression score

Results showed that we had to reject the null hypothesis and conclude that the mean depression scores are equal across the three states

1. Use inferences about individual treatment means where appropriate. What are your conclusions?

Solution

In this part, I tested for individual treatment means where I tested that the mean depression score is greater than 10 for all the three states.

The hypothesis are;

H₀: µ = 10

H₀: µ > 10

For each state

Results revealed that only New York showed mean depression scores as being significantly greater than 10 (M = 11.625, p-value < 0.05). The other two states Florida and North Carolina had though had depression scores greater than 10, the values were not significantly greater than 10 (M = 10.0250, p-value > 0.05 and M = 10.500, p-value > 0.05 respectively).