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Q1: Many companies manufacture products that are at least partially produced using chemica
stell). In many cases, the quality of the finished product is a function of the tempreture and pr
chemical reasctions take place, and whether the raw material is from one of the certain brand
manufacturer wants to model the quality (y) of a product as a function of the templrature (X1
which it is produced, and its brand. The data in the “Data” sheet in this document contains da
designed experiment involving these variables. Note that the assigned quality score can range
maximum of 100 for each manufactured product. The categorical variable equals to “Yes” if th
product is from certain brands. Note that categorical variables need to be transformed into nu
them in a regression.
a) Estimate a multiple regression equation that includes the three given explanatory variables
results in a new sheet in this document. Does the estimated equation fit the data well?
b) Write down the null hypothesis to test statistical significance of the coefficient estimates; a
for each coefficient. Based on the regression outputs, do you reject or fail to reject the null hy
mean? Interpret your results for each coefficient and variable.
c) Create an interruction term between tempreture and pressure (create a new data column t
with Pressure. You can use this formula: =Temperature*Pressure. Run the regression again no
variables; “Temperature,” “Pressure”, and “Temperature*Pressure.” Does the inclusion of inte
model’s goodness of fit?
d) For this new model, write down the null hypothesis to test statistical significance of the coe
seperate null hypothesis for each coefficient. Based on the regression outputs of this second m
to reject the null hypotheses? What does that mean? Interpret your results for each coefficien
e) How are your regression outputs of the second model different from the regressio outputs
roduced using chemicals (e.g., paint, gasoline, and
the tempreture and pressure at which the
ne of the certain brands. Suppose that a particular
of the templrature (X1), the pressure (X2) at
document contains data obtained from a carefully
quality score can range from a minimum of 0 to a
ble equals to “Yes” if the raw material of the
be transformed into numeric form before running
n explanatory variables. Report your regression
t the data well?
coefficient estimates; a seperate null hypothesis
ail to reject the null hypotheses? What does that
e a new data column that multiplies Temperature
he regression again now with three explanatory
oes the inclusion of interruction term improve the
significance of the coefficient estimates; a
utputs of this second model, do you reject or fail
sults for each coefficient and variable.
the regressio outputs of the first model?
Product
1
2
3
4
5
6
7
8
9
10
11
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15
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19
20
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Quality
56.46
61.98
91.57
65.19
70.91
78.21
71.55
81.89
44.96
23.52
40.23
81.83
85.97
67.83
88.59
59.42
79.66
96.04
86.18
44.92
53.08
61.45
73.84
36
60.96
49.54
38.35
81.02
57.99
60.95
77.08
56.74
49.52
76.61
63.07
66.56
63
54.89
52.2
56.3
85.62
66.83
58.34
Temperature
108.08
105.8
71.18
93.77
89.18
87.81
76.39
94.28
93.28
100.74
98.39
119.49
90.3
98.21
85.37
92.91
98.08
96.14
94.84
88.37
77.8
92.72
87.54
76.15
85.15
74.93
94.3
86.08
87.86
91.53
75.99
77.51
92
89.1
84.42
83.33
92.04
71.67
110.44
88.08
90.17
99.94
93.73
Pressure Branded
54.02 No
47.38 Yes
47.28 No
47.15 No
55.34 Yes
52.75 No
51.32 No
50.54 Yes
43.02 No
52.11 Yes
53.57 Yes
59.67 No
52.66 No
61.31 Yes
49.58 No
53.75 Yes
52.73 Yes
53.29 No
59.76 Yes
52.24 Yes
53.05 Yes
52.01 No
59.65 Yes
47.32 No
61.66 Yes
55.49 Yes
48.82 No
61.01 No
53.9 No
54.29 Yes
59.95 No
54.52 Yes
51.39 Yes
56.24 No
51.95 No
56.3 No
63.4 Yes
53.36 No
58.45 No
52.37 Yes
63.54 No
63.18 Yes
51.86 Yes
This is fictitious data.
44
45
46
47
48
49
50
69.45
66.35
61.85
67.17
80.11
93.16
66.54
82.36
93.61
93.27
95.56
87
87.74
95.69
56.36 Yes
53.37 Yes
55.32 Yes
52.87 No
46.4 Yes
53.26 No
51.35 No
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