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# Hypothesis test,Regression,Autocorrelation,Multicollinearity

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Construct a 95 per cent confident interval given the information below: A certain brand of fluorescent light tube was advertised as having an average illumination life-span of...
Given the following data from two independent samples from which the population standard deviation is known, conduct a two-tailed hypothesis test to determine if the first sample mean is smaller than the second sample mean, given a 0.10 level of significance...
Conduct a one-tailed hypothesis test given the information below: A test was conducted to determine whether gender of a spokesperson affected the likelihood that consumers would prefer a new product. A survey of consumers at a trade show employing a female spokesperson determined that...
Conduct a two-tailed hypothesis test given the information below: Assuming that the population standard deviations are unknown, but equal for male and female Grade Point Averages (GPAs), use the following sample data to test whether the averages are different at the 0.05 level of significance...
Answer questions (a) through (e) using the following information and output for multiple regression: A real estate investor has devised a model to estimate home prices in a new suburban development. Data for a random sample of 30 homes were gathered on the selling price of the home (\$ thousands), the home size (square feet), the lot size (thousands of square feet), and the number of bedrooms. The following multiple regression output was generated...

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## Statistics Problems - Regression Analysis, Autocorrelation, Multicollinearity

1. Suppose an appliance manufacturer is doing a regression analysis, using quarterly time-series data, of the factors affecting its sales of appliances. A regression equation was estimated between appliance sales (in dollars) as the dependent variable and disposable personal income and new housing starts as the independent variables. The statistical tests of the model showed large t-values for both independent variables, along with a high r2 value. However, analysis of the residuals indicated that substantial autocorrelation was present.

a. What are some of the possible causes of this autocorrelation?

b. How does this autocorrelation affect the conclusions concerning the significance of the individual explanatory variables and the overall explanatory power of the regression model?

c. Given that a person uses the model for forecasting future appliance sales, how does this autocorrelation affect the accuracy of these forecasts?

d. What techniques might be used to remove this autocorrelation from the model?

2. Suppose the appliance manufacturer discussed in Exercise 1 also developed another model, again using time-series data, where appliance sales was the dependent variable and disposable personal income and retail sales of durable goods were the independent variables. Although the r2 statistic is high, the manufacturer also suspects that serious multicollinearity exists between the two independent variables.

a. In what ways does the presence of this multicollinearity affect the results of the regression analysis?

b. Under what conditions might the presence of multicollinearity cause problems in the use of this regression equation in designing a marketing plan for appliance sales?

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