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Students in a management science class have just received their grades on the first test. The instructor has provided information about the first test grades in some previous classes as well as the final average for the same students. Some of these grades have been sampled and are as follows:
(a) Develop a regression model that could be used to predict the final average in the course based on the first test grade.
(b) Predict the final average of a student who made an 83 on the first test.
(c) Give the values of r and for this model. Interpret the value of in the context of this problem. Student 1 2 3 4 5 6 7 8 9 1st test grade 98 77 88 80 96 61 66 95 69 final average 93 78 84 73 84 64 64 95 76

Sagot :

fichoh

Answer:

A.) ŷ = 0.73986X + 18.98921

B.) 80

C.) r = 0.9205

Step-by-step explanation:

Given :

1st test grade (X) :

98

77

88

80

96

61

66

95

69

final average (Y) :

93

78

84

73

84

64

64

95

76

Using a linear regression calculator :

The model obtained is :

ŷ = 0.73986X + 18.98921

Student with x = 83

ŷ = 0.73986(83) + 18.98921

ŷ = 80.39759

ŷ = 80 (nearest whole number)

The R value is : 0.9205 which shows that there is a strong linear correlation between the first test grade and the final average a student Obtian in an exam because the r value is very close to 1.

R² = √0.9205 = 0.8473 ; this means about 84.73% of variation in final average can be explained by the regression line.

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