A gift card company has about 10 different coloured cards for sale. Since the colouring process is expensive they want reduce the number of colours. In order to decide which colour to be used they piloted as study by taking the NUMBER (X₁) of a COLOUR X₂ that sell the most and the REVENUE from different outlets. Partial Data Set n = 36. They chose blue, pink and green cards for the study. Revenue 78.8 73.8 Number 100 150 Colour P B

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6.4. The analyst ran the data again with only the observations relating to Blue and Green.
6.4.1. Give the dataset that he will use. Refer to the dataset given initially.
6.4.2. Show the new coding structure of the indicator variable Colour and show the new
amended partial data set. Also, give the general form of the new regression function to
run on the data.
6.4.3 Give the hypothesis statement and the test statistic formula for testing whether the two
lines are identical. (No calculations.)
6.4.4. If the regression in Question 6.4.3 has the following coefficients,
Ŷ = 5 + 4X₁ + 3X₂ - 2X₁X₂.
Interpret b₁.
Transcribed Image Text:6.4. The analyst ran the data again with only the observations relating to Blue and Green. 6.4.1. Give the dataset that he will use. Refer to the dataset given initially. 6.4.2. Show the new coding structure of the indicator variable Colour and show the new amended partial data set. Also, give the general form of the new regression function to run on the data. 6.4.3 Give the hypothesis statement and the test statistic formula for testing whether the two lines are identical. (No calculations.) 6.4.4. If the regression in Question 6.4.3 has the following coefficients, Ŷ = 5 + 4X₁ + 3X₂ - 2X₁X₂. Interpret b₁.
A gift card company has about 10 different coloured cards for sale. Since the colouring process is
expensive they want reduce the number of colours. In order to decide which colour to be used they
piloted as study by taking the NUMBER (X₁) of a COLOUR X₂ that sell the most and the
REVENUE from different outlets. Partial Data Set n = 36. They chose blue, pink and green cards
for the study.
Revenue
78.8
73.8
64.6
97.6
84.4
70.5
Number
100
150
69
79
140
120
Colour
P
B
G
...
G
P
B
X₁ = NUMBER of coloured cards sold
X₂ = COLOUR: P = pink, B = blue and G = green
Ŷ = REVENUE recorded in x R1000.00
The analyst expanded his analysis and SAS produced the following regression function.
= 6.21 + 1.03 X₁ + 41.3 X₂ + 22.7 X3 -0.703 X₁X₂ - 0.510X₁X3.
Transcribed Image Text:A gift card company has about 10 different coloured cards for sale. Since the colouring process is expensive they want reduce the number of colours. In order to decide which colour to be used they piloted as study by taking the NUMBER (X₁) of a COLOUR X₂ that sell the most and the REVENUE from different outlets. Partial Data Set n = 36. They chose blue, pink and green cards for the study. Revenue 78.8 73.8 64.6 97.6 84.4 70.5 Number 100 150 69 79 140 120 Colour P B G ... G P B X₁ = NUMBER of coloured cards sold X₂ = COLOUR: P = pink, B = blue and G = green Ŷ = REVENUE recorded in x R1000.00 The analyst expanded his analysis and SAS produced the following regression function. = 6.21 + 1.03 X₁ + 41.3 X₂ + 22.7 X3 -0.703 X₁X₂ - 0.510X₁X3.
Expert Solution
Step 1

In the given research problem, the variables under study are as follows:

X1= Number of coloured cards sold

X2=Colour of the card (Pink, Blue, Green)

Y^= Revenue

The regression model based on the partial data set of n=36 observations is:

Y^=6.21+1.03X1+41.3X2+22.7X3-0.703 X1X2-0.510X1X3

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