Question

Research into the relationship between hours of study and grades show widely different conclusions. A recent survey of graduates who wrote the Graduate Management Admissions Test (GMAT) had the following results.

Hours Studied Average Score

(Midpoint)

64 350

72 450

79 550

106 650

99 750

The Excel output for this regression is as following

SUMMART OUTPUT

____________________________

Regression Statistics

____________________________

Multiple R 0.919958

R Square 0.846322

Adjusted R Square 0.795097

Standard Error 71.57225

Observations 5

Anova

___________________________________________________________________________________________

DF SS MS F Sign. F

___________________________________________________________________________________________

84632.2 84632.2 16.521 0.0268

Regression. 1 4 4 4 6

15367.7 5112.58

Residual 3 6 7

Total 4 100000

___________________________________________________________________________________________

Coefficient Standard Lower Upper

s Error t Stat P-Value 95% 95%

___________________________________________________________________________________________

171.192 0.4921 411.24

Intercept -133.568 8 -0.78022 6 -678.38% 4

0.0268

X Variable 1 8.137715 2.00207 xxxxxx 6 1.7662 14.509

___________________________________________________________________________________________

a) How accurate is this regression at predicting GMAT scores base on hours studied? Explain.

b) What is the regression equation for this relationship?

c) Use the regression equation to predict the average score for each category of hours studies.

d) Calculate the t statistic to determine approximately how “significant” this regression is (note that the t may be greater than or less than the value from the t table).

Answer #1

Q1: From ANOVA table p- value = 0.0268

Since p-value is less than 0.05,we reject the null hypothesis and can say that the regression model is significant to predict the GMAT scores.

Coefficient of determination, r^{2} = 0.8463

So
about **84.63% variation** in the response variable
GMAT score explained by predictor variable hours studied.

--

Q2: Regression equation :

**ŷ = -133.5681 + (8.1377) x**

--

Q3:

X |
Y | Predicted score, ŷ |

64 | 350 | -133.5681 + (8.1377) * 64 = 387.2457 |

72 | 450 | -133.5681 + (8.1377) * 72 = 452.3474 |

79 | 550 | -133.5681 + (8.1377) * 79 = 509.3114 |

106 | 650 | -133.5681 + (8.1377) * 106 = 729.0297 |

99 | 750 | -133.5681 + (8.1377) * 99 = 672.0657 |

--

Q4: Test statistic:

t = b /se(b1) = 8.137715/ 2.00207 = **4.0647**

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.
ACT Score Study Data
Study Hours GPA ACT Score 1 2 19.91 1 2 19.69 2 2 25.52 2 3 29.67 2
4 29.77
A...

Thane Company is interested in establishing the relationship
between electricity costs and machine hours. Data have been
collected and a regression analysis prepared using Excel. The
monthly data and the regression output follow:
Month
Machine Hours
Electricity Costs
January
3,500
$
18,900
February
3,900
$
22,000
March
2,900
$
14,000
April
4,100
$
24,000
May
4,800
$
28,750
June
4,300
$
23,000
July
5,500
$
25,250
August
4,500
$
23,250
September
3,000
$
16,500
October
4,700
$
27,000
November...

A business is evaluating their advertising budget, and wishes to
determine the relationship between advertising dollars spent and
changes in revenue. Below is the output from their
regression.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.95
R Square
0.90
Adjusted R Square
0.82
Standard Error
0.82
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
3
23.188
7.729
11.505
0.020
Residual
4
2.687
0.672
Total
7
25.875
Coefficients
Std Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
83.91
2.03...

In models B through D, what seems to be the relationship between
the burglary rate and the percent of the 18-64 population who are
young adults (18-24)?
Select one:
a. It is difficult to describe the relationship; the young adult
variables were all significant at 5% in models B, C, and D, but the
signs and sizes of the coefficients were very different between
models.
b. Conclusions about the relationship between young adults and
the burglary rate are difficult to...

10. In Exercise 6, we examined the relationship between years of
education and hours of television watched per day. We saw that as
education increases, hours of television viewing decreases. The
number of children a family has could also affect how much
television is viewed per day. Having children may lead to more
shared and supervised viewing and thus increases the number of
viewing hours. The following SPSS output displays the relationship
between television viewing (measured in hours per day)...

The following data is used to study the relationship between
miles traveled and ticket price for a commercial airline:
Distance in miles:
300 400
450 500
550 600
800 1000
Price charged in $:
140 220
230 250
255 288
350 480
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.987
R Square
0.975
Adjusted R Square
0.971
Standard Error
17.352
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
70291.3
70291.3
233.4
4.96363E-06
Residual
6
1806.6
301.1
Total...

1. Jensen Tire & Auto is in the process of deciding whether
to purchase a maintenance contract for its new computer wheel
alignment and balancing machine. Managers feel that maintenance
expense should be related to usage, and they collected the
information on weekly usage (hours) and annual maintenance expense
(in thousands of dollars).
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.9272
R Square
0.8597
Adjusted R Square
0.8422
Standard Error
4.1466
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression...

True or false: at the 5% level of confidence the intercept is
significantly different from zero? SUMMARY OUTPUT Regression
Statistics Multiple R 0.98711 R Square 0.974387 Adjusted R Square
0.965849 Standard Error 47.4523 Observations 9 ANOVA df SS MS F
Significance F Regression 2 513960.7 256980.4 114.1262 1.68E-05
Residual 6 13510.32 2251.72 Total 8 527471.1 Coefficients Standard
Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -100.805 48.43281 -2.08133 0.082583 -219.316 17.70612
-219.316 17.70612 Well Depth...

] A partial computer output from a regression analysis using
Excel’s Regression tool follows. Regression Statistics Multiple R
(1) R Square 0.923 Adjusted R Square (2) Standard Error 3.35
Observations ANOVA df SS MS F Significance F Regression (3) 1612
(7) (9) Residual 12 (5) (8) Total (4) (6) Coefficients Standard
Error t Stat P-value Intercept 8.103 2.667 x1 7.602 2.105 (10) x2
3.111 0.613 (11)

Dep.=
Mileage
Indep.=
Cylinders
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
7.0000
ANOVA
Significance
df
SS
MS
F
F
Regression
12.4926
Residual
Total
169.4286
Standard
Coefficients
Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
38.7857
Cylinders
-2.7500
SE
CI
CI
PI
PI
Predicted
Predicted
Lower
Upper
Lower
Upper
x0
Value
Value
95%
95%
95%
95%
4.0000
1.9507
6.0000
1.1763
Is there a relationship between a car's gas
MILEAGE (in miles/gallon) and its...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 14 minutes ago

asked 40 minutes ago

asked 53 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago