Question

The data below are the final exam scores of 10 randomly selected history students and the number of hours they slept the night before the exam. Find the equation of the regression line for the given data. What would be the predicted score for a history student who slept 7 hours the previous night? Round your answer to the nearest whole number. Use the following values to speed up the calculations: x? = 4.2, ?x = 42, ?x² = 208, SSxy = 165.4, ? = 76.8 Hours, x | 3 | 5 | 2 | 8 | 2 | 4 | 4 | 5 | 6 | 3 Scores, y | 65 | 80 | 60 | 88 | 66 | 78 | 85 | 90 | 90 | 66 ? = -5.044x + 56.11; Y(7) = 20.8 ? = 5.234x + 54.82; Y(7) = 91.5 ? = 5.234x + 54.82; Y(4.2) = 76.8 ? = 0.198x + 56.11; Y(7) = 57.5 None of these ? = 35.5x - 55.33; Y(4.2) = 93.8

          The data below are the final exam scores of 10 randomly selected history students and the
number of hours they slept the night before the exam. Find the equation of the regression line
for the given data. What would be the predicted score for a history student who slept 7 hours
the previous night? Round your answer to the nearest whole number.
Use the following values to speed up the calculations:
x? = 4.2, ?x = 42, ?x² = 208, SSxy = 165.4, ? = 76.8

Hours, x | 3 | 5 | 2 | 8 | 2 | 4 | 4 | 5 | 6 | 3
Scores, y | 65 | 80 | 60 | 88 | 66 | 78 | 85 | 90 | 90 | 66

? = -5.044x + 56.11; Y(7) = 20.8
? = 5.234x + 54.82; Y(7) = 91.5
? = 5.234x + 54.82; Y(4.2) = 76.8
? = 0.198x + 56.11; Y(7) = 57.5
None of these
? = 35.5x - 55.33; Y(4.2) = 93.8

Show more…

The data below are the final exam scores of 10 randomly selected history students and the
number of hours they slept the night before the exam. Find the equation of the regression line
for the given data. What would be the predicted score for a history student who slept 7 hours
the previous night? Round your answer to the nearest whole number.
Use the following values to speed up the calculations:
x? = 4.2, ?x = 42, ?x² = 208, SSxy = 165.4, ? = 76.8

Hours, x | 3 | 5 | 2 | 8 | 2 | 4 | 4 | 5 | 6 | 3
Scores, y | 65 | 80 | 60 | 88 | 66 | 78 | 85 | 90 | 90 | 66

? = -5.044x + 56.11; Y(7) = 20.8
? = 5.234x + 54.82; Y(7) = 91.5
? = 5.234x + 54.82; Y(4.2) = 76.8
? = 0.198x + 56.11; Y(7) = 57.5
None of these
? = 35.5x - 55.33; Y(4.2) = 93.8

Added by Antonio N.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

02/07/2023

Step 1

4 - 42 \times 76.8}{10 \times 208 - 42^2} \] \[ b = \frac{1654 - 3225.6}{2080 - 1764} \] \[ b = \frac{-1571.6}{316} \] \[ b = -4.9772 \] Show more…

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The data below are the final exam scores of 10 randomly selected history students and the number of hours they slept the night before the exam. Find the equation of the regression line for the given data. What would be the predicted score for a history student who slept 7 hours the previous night? Round your answer to the nearest whole number. Use the following values to speed up the calculations: x̄ = 4.2, Σx = 42, Σx^2 = 208, SSxy = 165.4, ȳ = 76.8.

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Transcript

00:01 Hello students according to the given question we have to find which option is correct.

00:07 So they have given the values n is equal to 10 and summation x will be equal to 42 and ssxy will be equal to 165 .4.

00:23 So here by the given data we can say that summation xy value will be equal to 3391.

00:32 And summation y will be equal to 768 from the given data.

00:39 So x bar is given as 4 .2 and y bar is written as 76 .8.

00:47 Now we have to find the straight line equation that is y will be equal to ax plus b so it can also be written as y is equal to mx plus.

01:00 So now we have to find the a value and b value.

01:08 A will be equal to the formula summation x into summation y minus n into summation xy is divided by summation x whole square minus n summation x square.

01:25 So by substituting we get a will be equal to 42 into 768 minus 10 into 3391 is divided by 42 square minus 10 into 208.

01:45 So by solving it we get a will be equal to minus 1654 is divided by minus 316.

01:54 So then a will be equal to the value 5 .23442.

02:02 Now we have to calculate b value.

02:05 B equal to the formula summation x into summation x minus summation y minus summation y into summation y into summation x squared is divided by summation x whole square minus n summation x square by substituting we get b is equal to 42 into 3391 minus 768 into 208 is divided by 42 square minus 10 into 208...

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