Description
Q1: Many companies manufacture products that are at least partially produced using chemicals (e.g., paint, gasoline,
and stell). In many cases, the quality of the finished product is a function of the tempreture and pressure at which the
chemical reactions take place, and whether the raw material is from one of the certain brands. Suppose that a
particular manufacturer wants to model the quality (y) of a product as a function of the templature (X1), the pressure
(X2) at which it is produced, and its brand. The data in the “Data” sheet in this document contains data obtained from a
carefully designed experiment involving these variables. Note that the assigned quality score can range from a minimum
of O to a maximum of 100 for each manufactured product. The categorical variable equals to “Yes” if the raw material of
the product is from certain brands. Note that categorical variables need to be transformed into numeric form before
running them in a regression.
a) Estimate a multiple regression equation that includes the three given explanatory variables. Report your regression
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 seperate null hypothesis
for each coefficient. Based on the regression outputs, do you reject or fail to reject the null hypotheses? What does that
mean? Interpret your results for each coefficient and variable.
c) Create an interruction term between tempreture and pressure (create a new data column that multiplies
Temperature with Pressure. You can use this formula: Temperature *Pressure. Run the regression again now with three
explanatory variables; “Temperature,” “Pressure”, and “Temperature *Pressure.” Does the inclusion of interruction term
improve the model’s goodness of fit?
d) For this new model, write down the null hypothesis to test statistical significance of the coefficient estimates; a
seperate null hypothesis for each coefficient. Based on the regression outputs of this second model, do you reject or fail
to reject the null hypotheses? What does that mean? Interpret your results for each coefficient and variable.
e) How are your regression outputs of the second model different from the regressio outputs of the first model?
the data is provided in an excal sheet
Note: it is an urgent request and we can’t postpone further than the timing requested
please prevoid the answers and how you answered them step by step or record the solving pr
Unformatted Attachment Preview
Product
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Quality
Temperature
62.99
88.28
56.53
82.93
60.2
86.29
91.15
84.82
40.79
89.45
39.38
91.84
64.28
104.04
56.36
75.45
52.68
99.93
67.83
88.25
104.24
86.1
50.42
93.97
82.92
90.52
25.42
94.24
83.69
98.85
69.75
91.66
69.53
86.53
18.48
96.61
56.97
80.73
75.13
105.8
69.73
89.03
50.21
90.92
84.77
89.04
107.04
88.75
66.21
83.3
51.13
88.03
72.41
95.73
90.19
111.18
61.84
91.22
42.93
101.89
84.94
81.08
67.21
76.52
66.38
83.53
66.27
83.67
83.52
96.21
75.82
77.86
85.93
85.5
67.62
103.8
72.14
85.38
29.69
77.08
51.77
83.34
42.74
92.57
59.22
78.53
22.64
84.79
31.18
85.82
40.51
80.24
Pressure Branded
50.5 Yes
60.94 Yes
60.19 No
57.7 No
49.6 Yes
51.84 Yes
55.04 Yes
50.47 No
48.54 Yes
48.89 Yes
61.43 No
56.51 No
56.54 No
55.78 No
61.85 Yes
52.44 No
56.45 No
57.67 Yes
53.03 Yes
50.44 Yes
53.95 No
56.02 No
60.53 No
48.75 Yes
57.09 Yes
48.03 No
54.01 Yes
51.05 Yes
53.85 Yes
51.77 No
55.33 No
48.86 No
53.45 No
49.83 No
52.51 Yes
57.29 No
58.23 Yes
54.26 No
50.55 No
53.6 Yes
56.15 Yes
52.01 No
51.38 No
55.06 No
51.52 No
51.39 Yes
47
48
49
50
100.08
59.79
63.74
55.27
82.77
70.64
93.66
84.51
56.9 Yes
58.04 Yes
48.7 Yes
60.76 Yes
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