3. The table shows the test scores and the sleep averages of several students . Test Score ( % ) 88 75 | 76 | 92 | 96 | 94 | 83 90 99 Average Sleep ( h ) 76.5 6 7.5 8 7 | 6.5 8 8.5 65 77 88 | 82 5 7 9 8 83 9497 8.5 8.5 9 ( a ) Write the least squares regression equation that models the data . Let x = the test score and y = average sleep . ( b ) Use the equation to determine the approximate test score of a student who sleeps an average of 8 hours a night . Show your work Answer :

ŷ = 0.09118X - 0.35873 ; 91.67%

Step-by-step explanation:

Given the following :

Test score (x) :

88

75

76

92

96

94

83

90

99

65

77

88

82

83

94

97

Average sleep (Hr) (y) :

7

6.5

6

7.5

8

7

6.5

8

8.5

5

7

9

8

8.5

8.5

9

Using the online linear regression calculator :

The linear model obtained is :

ŷ = 0.09118X - 0.35873

Comparing the output with the linear model function:

ŷ = mx + c

ŷ = dependent / predicted variable

m = gradient or slope = 0.09118

X = Independent variable

c = intercept(point where the line of best fit intersects the y - axis) = 0.35873

B) approximate test score of a student who sleeps an average of 8 hours a night

Here, ŷ = dependent variable = 8hrs

ŷ = 0.09118X - 0.35873

8 = 0.09118X - 0.35873

0.09118X = 8 + 0.35873

X = 8.35873 / 0.09118

X = 91.672844

Approximate test score = 91.67% = 92%

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step-by-step explanation: