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    Regression, ANOVA, Hypothesis

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    Problem 1 A,B,C Inc. produces fresh, a brand of liquid laundry detergent. In order to more effectively manage its inventory and make revenue projections, the company would like to like to better predict demand for Fresh. The company has established the flowing demand equation:
    Demand = Bo + B1FreshPrice + B2ComPrice + B3AdvExpend
    Your Minitab Output follows:

    Regression Analysis: Demand versus FreshPrice, ComPrice, AdvExpend
    The regression equation is
    Demand = 7.59 - 2.36 FreshPrice + 1.61 ComPrice + 0.501 AdvExpend
    Predictor Coef SE Coef T stat Pvalue
    Constant 7.589 2.445 3.10 0.005
    FreshPrice -2.3577 0.6379 -3.70 0.001
    ComPrice 1.6122 0.2954 5.46 0.000
    AdvExpend 0.5012 0.1259 3.98 0.000
    S = 0.234669 R-Sq = 89.4% R-Sq(adj) = 88.1%
    Analysis of Variance
    Source DF SS MS F Sign F
    Regression 3 12.0268 4.0089 72.80 0.000
    Residual Error 26 1.4318 0.0551
    Total 29 13.4586
    Source DF Seq SS
    FreshPrice 1 2.9631
    ComPrice 1 8.1907
    AdvExpend 1 0.8729

    Unusual Observations

    Obs FreshPrice Demand Fit SE Fit Residual St Resid
    5 3.60 9.3300 8.8164 0.0864 0.5136 2.35R

    R denotes an observation with a large standardized residual.
    Predicted Values for New Observations

    Obs Fit SE Fit 95% CI 95% PI
    1 8.4107 0.0469 (8.3143, 8.5070) (7.9188, 8.9025)

    Values of Predictors for New Observations
    Obs FreshPrice ComPrice AdvExpend
    1 3.70 3.90 6.50

    a. Write out the regression equation.
    b. Predict the Demand when FreshPrice is 3.70, ComPrice is 3.90 and AdvExpend is 6.50.
    c. Using the data from #1 above:
    1. Report R-Sq and Adj R-SQ. Explain there differences and explain their meaning in the context of this problem.
    2. Test the entire Model for significance. That is, the F test. Let alpha equal .05.

    d. Using the t tests on each of the independent variables and also the p values.

    PROBLEM 5 Given the following data from two independent data sets, conduct a hypothesis test to determine if the means are statistically equal using alpha=0.05. Do NOT do a confidence interval.

    n1 = 10 n2 = 10
    xbar1= 121.92 xbar2 = 114.81
    s1=1.40 s2 = 1.84

    PROBLEM 6. American Demographics (Jan. 2002) reported the results of a survey on the planning habits of men and women. In response to the question, "What is your preferred method of planning and keeping track of meetings, appointments and deadlines?" 56% of the men and 46% of the women answered "keep them in my head". A nationally representative sample of 1000 adults participated in the survey; therefore, assume that 500 were men and 500 were women.
    a. Set up the null and alternative hypothesis for testing whether the percentage of men who prefer keeping track of appoints in their heads is larger than the corresponding percentage of women.
    b. Compute the test statistic for the test.
    c. Give the rejection region for the test using alpha = .01.
    d. Make the appropriate conclusion.

    PROBLEM 7 A study compared three different display panels for use by air traffic controllers. Each display panel was tested in a simulated emergency condition: 12 highly trained air traffic controllers took part in the study. Four controllers were randomly assigned to each display panel. The time (in seconds) deeded necessary to stabilize the emergency conditions were recorded. The results of the computer analysis is below. Carry out the appropriate statistical test to determine if the average time necessary to stabilize the emergency conditions is the same for the three methods. Let alpha = .05. Show the 5 steps for the One Way ANOVA or Single factor ANOVA:

    One-way ANOVA: Panel A, Panel B, Panel C

    Source DF SS MS F Sign f
    Factor 2 500.17 250.08 30.11 0.000
    Error 9 74.75 8.31
    Total 11 574.92

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    Solution Summary

    Step by step method for regression analysis,ANOVA and hypothesis testing are discussed here. Regression coefficients, coefficient of determination, scatter diagram , significance of regression model, test statistic, critical value and p value are explained in the solution.