Question 2
Nine experts rated four brands of coffee in a tasting experiment. A rating on a seven-point scale (1 – worst, 7 – excellent) is given for each of the following four characteristics: taste, aroma, richness, and acidity. The following table displays the ratings (total scores, summed over all four characteristics).
Coffee brand
|
Expert |
A |
B |
C |
D |
|
1 |
24 |
26 |
25 |
22 |
|
2 |
27 |
27 |
26 |
24 |
|
3 |
19 |
22 |
20 |
16 |
|
4 |
24 |
27 |
25 |
23 |
|
5 |
22 |
25 |
22 |
21 |
|
6 |
26 |
27 |
24 |
24 |
|
7 |
27 |
26 |
22 |
23 |
|
8 |
25 |
27 |
24 |
21 |
|
9 |
22 |
23 |
20 |
19 |
At the 0.05 level of significance, is there evidence of a significant difference between the median ratings of the four brands of coffee?
Select the appropriate procedure and state the statistic.
Question 3
We are conducting a simple linear regression (SLR) model fitting study based on 15 data pairs. Fill in the missing data in the following partially given ANOVA table. (Degrees of freedom denoted by df below.)
df SS MS F Significance
Regression ? 21.86043 ? ? ?
Residual ? ? ?
Total ? 33.25057
Based on your ANOVA table, decide if the corresponding SLR model is statistically significant (i.e., it gives sufficient explanation of the model outcome based on the input variable), or not.
Question 4
Consider the following residual plot for a set of data collected over 15 consecutive weeks.
Do you think that there is autocorrelation between these residuals? If yes, then select the appropriate statistic to answer this question. See in the Excel workbook under Question 4 a set of residuals that approximately correspond to the figure above. Calculate in Excel the value of the chosen statistic and compare it to the critical values 1.08 and 1.36 that are provided (by assumption, known or retrieved from a table) to you. Draw your conclusion.
Question 5
To analyze the real estate market in a city, a large national real estate company has collected samples of recent residential sales. The data are stored in the Excel file, see the tab Question5.
5.1. Find the multiple linear regression equation.
5.2. Based on the result and your intuition, which explanatory variable could be left out from the model? Skip that variable and repeat the multiple linear regression model setup. Which explanatory variable seems to be the most important now?
5.3. Using the most important variable that you select, perform SLR.
5.4. Based on your results, do you think that this model has a good overall predictive value?
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