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Bus 310 Final Exam

Name:____________________________

You work for Big Kuhuna Malasadas and you are interested in how best to increase profit from sales of your malasadas. You have data collected over a series of 15 weeks on the following variables to help you make some decisions. Price: The selling price of one dozen malasadas ($ per dozen) Advertising: Amount spent on advertising ($000’s per month) Sales: number of malasadas sold per week Holiday: 1=holiday, 0=no holiday Season: winter, spring, summer, fall

Use the information above to answer the following questions:

1.

The regression model for this problem

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(a) Write out the regression formula in terms of the dependent variable Y and independent variables X1, X2, X3 (ignore Season for now). Be sure to define what each variable is including units and their corresponding coefficients. Model: Y=b0+b1x1+b2x2+b3x3+-E Regression : Y=290-13x1+42x2+75x3+-32 (standard error) For every ($1000) advertising increase, increase malasadas by 48. If there’s a holiday within the week, malasada sales increase by 76. (b) Set up hypotheses and interpret results to test if any of the independent variables are related to Sales with 95% confidence. H0: b1=b2=b3=0 H1: at least one b doesn’t equal 0 There’s sufficient evidence to reject the null hypothesis. We’re almost 100% confident that at least 1 variable H0: b1=0 H1: b1 doesn’t =0 At .12, it’s not significant. Fail to reject, less than 95% H0: b2=0 H1: b2 doesn’t =0 At .03, there’s sufficient evidence to reject the null. 97% confident in alternate so advertising is significant to the model H0: b3=0 H1: b3 doesn’t =0 At .002, there’s sufficient evidence to reject the null. Almost 100% confident in alternate so advertising is significant to the model (c) Is the assumption of linearity good? If so why? If not, why not and explain what this might mean for the validity of the model. Linearity checks out. (residuals of x-look at look for price and advertising[x1&x2]) (no smile/frown)If there’s issues w linearity, force it to be linear through the quadratic model to square the data. Adjusted r2=sales of malasadas is explained by price, advertising and holidays. I N E (d) Is there evidence that there are factors missing (i.e. missing independent variables)? Why or why not? (e) Is there an interaction between Holiday and Advertising? Explain if it is a significant predictor for Sales. Hint: look at the very last table in the results given. How much confidence would we have if we wanted to include all independent variables (except Season) in the model? Explain why we might want to keep a variable in the model that has lower than 90% confidence. By including all the independent variables in the model, we can be 88% confident (1-p-value of price bc highest value) We’d want to keep price in the model bc price matters or there won’t be any profit.

2.

Interpret the meaning of the slope with 95% confidence for Price. Indicate if it is a significant predictor or not. Hint: Look at the confidence interval for the slope. Do not forget about “holding all other variables constant”

3.

Which Regression Statistic most directly addresses how far off the prediction will typically be? Interpret this statistic for this data.

4.

For the Next two Cases Interpret the results. Include all relevant information such as hypothesis, confidence levels, p-values, and assumptions as applicable, interpretations, etc . Use the format discussed in class and used in the homework.

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Case 1: Reason for Staying at Waikiki Hotels The parent company of three Waikiki hotels wishes better understand why visitors choose certain of their Hotels. A survey of 200 random hotel guests at the Aloha Spirit, Hula Inn, and Bradda Charlie’s hotel were asked what their primary reasons were for selecting their hotel. Following results from data was gathered:

5. The parent company is most interested in the reasons that cause visitors to select a particular hotel. That is, given that a visitor selected a particular hotel, what are the most likely and least likely reasons for their choice? Using the results above write a report on what can be concluded about the impact (relationship) of reason on hotel choice and the statistics used to make these conclusions. Be sure to discuss which groups have the most influence. Hint: this is similar to the Ch. 11.3 example and problem 11.36 from PS6. To answer the question does it make more sense to consider the frequency visitors choose a hotel given a reason (the table on the left at the bottom of the results above), or the frequency of a reason given a hotel (the table on the right at the bottom of the results above)? Pie1=pie2=pie3 At least one doesn’t equal 0 Almost 100% confident in alternate Aloha Spirit has a negative dependency for price and a positive dependency for location. For Bradda Charlie’s, it has a positive price dependency and a negative location dependency (column vs row) Table on left says what drives customers to choose each hotel. Then the table on the right says- more on price for BC and more on location for AS.

Case 2: Golf Club Performance 3

You want to see if three different golf clubs yield different distances for the same golfball. You randomly select five measurements from trials on an automated driving machine for each club. At the 0.05 significance level, is there a difference in mean distance? Be sure to: a)write out the appropriate hypothesis and define what specifically the population parameters (e.g. population means or population proportions) are being tested H0: mew1=mew2=mew3 H1: at least one is statistically sig diff b)Interpret the results of the test and state the actual confidence. Sufficient . Almost 100% to go with alternate. c)Check any needed assumptions such as Normality, equal variances. If there are assumptions that are of questionable validity, discuss how this may affect the reliability of the results and what might be done to improve reliability (if anything). I: random selection so it’s given. N: Skew and kurt are outside -1 and 1. Since p-value’s extremely low, we can assume normality. Test is still good. E: equal variance checks out. d) Discuss what the results say about which clubs have better performance.

6. Using the results above write a report on what can be concluded about the difference in distances the clubs drive a golfball. Group 2: 205 Group 1: 247 Group 3: 252 (arranged least to farthest distance) Critical range: between 1 and 2 means diff, 1 and 3-means not diff, 2 and 3, means diff. So, do group 3 as we’re the ball went the farthest. Golf club 1’s SD’s 12, so it’d go above/below 247 (distance). If based on accuracy, club 3 (always look for ‘means aren’t different’)

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