Question

Applications I

Consider the following data representing the total time (in hours)
a student spent on reviewing for the Stat final exam and the actual
score on the final. The sample of 10 students was taken from a
class and the following answers were reported.

time score

0 23

4 30

5 32

7 50

8 45

10 55

12 60

15 70

18 80

20 100

Part 1: Use the formulas provided on the 3rd formula sheet to
compute the following quantities. Open an Excel spreadsheet and
write the table with data given above. Add columns for x2, y2, and
xy, as well as the last row for Σ. For each of the following
quantities, write the formula for it in a cell and evaluate
it.

(a) Find the sample correlation coefficient r.

(b) Find the slope b1 of the sample regression line.

(c) Find the y-intercept b0 of the sample regression line.

(d) What is the equation of the sample regression line?

(e) Find the predicted final exam score for a student who spent 14
hours reviewing before the final.

(f) Find the predicted final exam score for a student who spent 15
hours reviewing before the final.

(g) What is the difference between the observed and the predicted
final exam score for a studentwho spent 15 hours reviewing before
the final?

(h) Find the total sum of squares SST.

(i) Find the sum of squares error SSE.

(j) Find the sum of squares regression SSR.

(k) Use the answers from (h)-(j) to confirm that SST = SSR +
SSE.

(l) Find the coefficient of determination R2.

(m) Use your answers for (a), (b) and (l), to confirm that r
.

(n) What proportion of variation is explained using the regression
model?

(o) Find the standard error of the estimate se.

(p) Find the standard error of the regression slope sb.

(q) Does the amount of time spent reviewing for the final affect
the final exam score? Use the sample provided above and the
significance level of 0.05.

(hint: perform the hypothesis test for H0 : β1 = 0 vs. H1 : β1 =
0.)6

Part 2: Find and use Excel built-in-functions to check your answers
for r, b1, and b0. Next to each cell from Part 1, calculate these
three quantities using Excel built-in-functions and confirm your
answers from Part 1.

(hint: for example, for r the Excel built-in function is
”CORREL”)

Part 3: Bellow your answers from Parts 1 and 2, perform the
regression analysis using Excel built-in-module which can be found
under ”DATA” → ”Data Analysis” → ”Regression” and double check your
answers from Part 1. Draw the scatter plot of the data and, by
visually observing the graph, determine if there is a linear
relationship between the amount of time a student spent reviewing
for the final exam and the actual score on the final.

Save your Excel book.

Answer #1

Statistical Analysis for Business Applications I
Consider the following data representing the total time (in hours)
a student spent on reviewing for the Stat final exam and the actual
score on the final. The sample of 10 students was taken from a
class and the following answers were reported.
time score
0 23
4 30
5 32
7 50
8 45
10 55
12 60
15 70
18 80
20 100
Part 1: Use the formulas provided on the 3rd...

The following data set shows the entrance exam score (Verbal
GMAT) for each of eight MBA students along with his or her grade
point average (GPA) upon graduation.
GMAT: 300 280 270 270 360 280 290 310
GPA: 3.7 2.9
3.2 3.2 3.9
2.9 3.8 2.9
a. Calculate the SST./ SST=
___________(Round to three decimal places as needed.)
b. Partition the total sum of squares into the SSR and
SSE. SSR=_____________
SSE= ____________. (Round to three decimal places as
needed.)...

The following data show the brand, price ($), and the overall
score for six stereo headphones that were tested by a certain
magazine. The overall score is based on sound quality and
effectiveness of ambient noise reduction. Scores range from 0
(lowest) to 100 (highest). The estimated regression equation for
these data is
ŷ = 23.528 + 0.315x,
where x = price ($) and y = overall score.
Brand
Price ($)
Score
A
180
76
B
150
71
C
95...

The following data show the brand, price ($), and the overall
score for 6 stereo headphones that were tested by Consumer Reports.
The overall score is based on sound quality and effectiveness of
ambient noise reduction. Scores range from 0 (lowest) to 100
(highest). The estimated regression equation for these data is Y=
22.153 + 0.328 x, where x = price ($) and y = overall score. Brand
Price ($) Score Bose 170 76 Skullcandy 160 71 Koss 95 62...

The following data show the brand, price ( $ ) and the overall
score for 6 stereo headphones that were tested by Consumer
Reports. The overall score is based on sound quality and
effectiveness of ambient noise reduction. Scores range from 0
(lowest) to 100 ( highest) The estimated regression equation for
these data is y-hat = 25.147 + 0.299x , where x = price ( $ ) and y
= overall score.
Brand
Price
Score
Bose
180
75
Scullcandy...

The following data show the brand, price ($), and the overall
score for 6 stereo headphones that were tested by Consumer Reports.
The overall score is based on sound quality and effectiveness of
ambient noise reduction. Scores range from 0 (lowest) to 100
(highest). The estimated regression equation for these data is ŷ =
25.036 + 0.3x, where x = price ($) and y = overall score.
Brand Price Score Bose 180 76 Scullcandy 150 71 Koss 85 61
Phillips/O'Neill...

The following data
show the brand, price ($), and the overall score for 6 stereo
headphones that were tested by Consumer Reports. The overall score
is based on sound quality and effectiveness of ambient noise
reduction. Scores range from 0 (lowest) to 100 (highest). The
estimated regression equation for these data is ŷ = 25.854 +
0.291x, where x = price ($) and y = overall score.
Brand
Price
Score
Bose
170
75
Scullcandy
160
71
Koss
95
62
Phillips/O'Neill...

The following data set shows the entrance exam score (Verbal
GMAT) for each of eight MBA students along with his or her grade
point average (GPA) upon graduation.
GMAT
300
300
250
290
350
280
300
300
GPA
3.6
2.9
3.1
3.3
3.9
3.1
3.7
2.9
A linear regression on the data gives the equation below.
Complete parts a through d below.
Predicted GPA equals 0.872390 plus 0.008237 left parenthesis
GMAT right parenthesis
partition the total sum of squares...

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 spent 15 hours the previous night? Is this a reasonable
question? Round your predicted score to the nearest whole number.
Round the regression line values to the nearest hundredth.
Hours, X, 3...

The following data was collected to explore how the average
number of hours a student studies per night and the student's GPA
affect their ACT score. The dependent variable is the ACT score,
the first independent variable (x1) is the number of hours spent
studying, and the second independent variable (x2) is the student's
GPA.
Study hours
GPA
ACT score
0
2
17
1
2
19
5
2
28
5
3
29
6
4
31
Find the p-value for the...

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