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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

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8

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10

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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

Student Name:

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a)

b)

c)

d)

e)

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