Question

We are considering a launch of a new type of raisin into the packaged raisin market. To do so, we collected product ratings on a 1-10 Likert-scale from consumers utilizing the following attributes and corresponding levels,

Attribute	Level1	level 2	level 3	level 4
Rasin Chewiness	low	medium	high	n/a
Rasin Color	white	grey	brown	black
Packaging Size	small	large	n/a	n/a
Free Gift	no	yes	n/a	n/a
Raisin Aroma	none	medium	heavy	n/a
Price Compared to Market Leader	lower	same	higher	n/a

Please base your answer to the following questions on this data. Note that each attribute is coded numerically. For instance, for Chewiness (Low =1, Medium =2, High =3) and similarly for the other attributes reading left to right in the table above.

For each of the attributes, we code the levels into multiple dummy variables to include in our regression. The variables we used are as follows:

Chew1 Chew2 Level 1 1 0 Level 2 0 1 Level 3 0 0 SizeLarge Level 1 0 Level 2 1 Aroma1 Aroma2 Level 1 1 0 Level 2 0 1 Level 3 0 0

Color1 Color2 Color3 Level 1 1 0 0 Level 2 0 1 0 Level 3 0 0 1 Level 4 0 0 0 GiftDummy Level 1 0 Level 2 1 Price1 Price2 Level 1 1 0 Level 2 0 1 Level 3 0 0

Note that for each category, the number of variables is equal to the number of levels – 1.

For example, for chewiness, we only need 2 dummy variables to show 3 levels:

• Chew1 = 1 and Chew2 = 0 indicates level 1 of chewiness.
• Chew1 = 0 and Chew2 = 1 indicates level 2 of chewiness.
• If neither Chew1 or Chew2 are 1 that only leaves level 3 of chewiness.

Regression Results from creating dummy variables

Coefficents	beta	std. error	t-value	p-value
intercept	5.2991	0.3240	16.353	0.0000
chew 1	-0.8659	0.2437	-3.5535	0.0006
chew 2	-0.3461	0.2438	-1.4195	0.1593
color 1	0.1211	0.2871	0.4218	0.6742
color 2	0.2145	0.2802	0.7657	0.4459
color 3	0.4799	0.2696	1.7801	0.0785
Size large	0.8992	0.2000	4.4969	0.0000
gift dummy	0.0916	0.2099	0.4365	0.6635
aroma 1	0.5468	0.2563	2.1334	0.0357
aroma 2	0.9715	0.2327	4.1742	0.0001
Price 1	0.6548	0.2157	3.0362	0.0032
Price 2	0.3237	0.2895	1.1180	0.2666

Residual standard error: 0.9418 on 88 degrees of freedom

Multiple R-Squared: 0.4276

F-statistic: 5.976 on 11 and 88 degrees of freedom, the p-value is 3.412e-007

1. Write down the model that was estimated in the regression, with the name of the variables and their coefficients in the model.
2. What Likert rating score would you predict for a raisin product that has Low Chewiness, Grey Raisins, Large Package Size, Free Gift, Medium Aroma, and the Same Price as the Market Leader? You may round your answer to the nearest integer.
3. What product has the highest predicted rating score?
4. Would you necessarily introduce this product, the one from previous part, if you were the decision maker?  Why or why not?
5. Suppose that the predicted market share of product j is proportional to R_j; that is market share, where R_jis the predicted Likert rating of product j. What would the predicted market share be if the product described in part b were introduced into the market consisting of current products i, ii, iii? The market currently contains the following three products:
   1. High Chewiness, Grey Raisins, Small Package Size, No Free Gift, Medium Aroma, and Same Price as the Market Leader’s (Likert =6.81)
   2. Low Chewiness, Brown Raisins, Small Package Size, Free Gift, Medium Aroma, and Same Price as the Market Leader’s (Likert =6.30)
   3. Medium Chewiness, Black Raisins, Large Package Size, No Free Gift, No Aroma, and Lower Price than the Market Leader’s (Likert =7.05)
6. Do the product attributes (as a whole) provide significant predictive power for the rating scores? Justify your answer.
7. Which product attributes, if any, have no statistically significant explanatory power for rating scores? State clearly how you arrived at your answer.

Answer 1

We are considering a launch of a new type of raisin into the packaged raisin market. To do so, we collected product ratings on a 1-10 Likert-scale from consumers utilizing the following attributes and corresponding levels,