# Q1 by gegeshandong

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```									MATH 205 Lab#3 Q1                                                                Name:                           PETER ABELS 201002080

By hand               m=            -3250                                        By trendline              m=                                -1770.9839
b=            21500                                                                  b=                                     18363

Price       Quantity        By Hand           Error        SE by Hand                           Trendline          Error            SE by Trendline
\$2.00        15,000         15,000                -               -                           14821.0322                   (179)           32,029
\$2.20        14,350         14,350                -               -                                14467                    117            13,651
\$2.35        14,192         13,863               (330)       108,570                               14201                      9                84
\$2.50        13,674         13,375               (299)        89,401                               13936                    262            68,403
\$2.80        13,666         12,400             (1,266)     1,602,756                               13404                   (262)           68,516
\$3.00        12,999         11,750             (1,249)     1,560,001                               13050                     51             2,606
Sum:            (3,144)     3,360,728                                Sum:                     (2)          185,289

Which one has less error?                                     X                  X2              Y                Y2                   X*Y
The method using the linear regression equation                        \$2.00            \$4.00           15,000       225,000,000              30000.00
has less error. Using the sum of squared errors                        \$2.20            \$4.84           14,350       205,922,500              31570.00
as a determinant, using linear regression it is                        \$2.35            \$5.52           14,192       201,412,864              33351.20
quite signficantly close to 0 compared to the                          \$2.50            \$6.25           13,674       186,978,276              34185.00
\$2.80            \$7.84           13,666       186,759,556              38264.80
method of by hand.
\$3.00            \$9.00           12,999       168,974,001              38997.00
Predicted                                                             \$14.85           \$37.45           83,881     1,175,047,197             206368.00

Price       Quantity
\$2.15        14555

Place Chart Here

15,500

15,000

14,500

14,000

13,500
y = -1771x + 18363
R² = 0.922
13,000

12,500
\$0.00    \$0.50     \$1.00       \$1.50       \$2.00      \$2.50        \$3.00     \$3.50
MATH 205 Lab#3 Q2                                                  Name:              PETER ABELS 201002080

% Bonus    Sales ('00s)
0            3
1            4
2            8          This trendline is a good fit as made
3           10          evident by the R2 value which
4           15          indicates the line is over 98%
5           18          accurate. This is a strong positive
6           20          correlation.
7           22
8           27
9           28

Chart showing scatter plot and linear trendline with equation and R^2 value

35

30

25

20
y = 2.9636x + 2.1636
R² = 0.9892
15

10

5

0
0           2            4              6               8                  10
MATH 205 Lab#3 Q3                                        Name:       PETER ABELS 201002080

2
Person         Rank 1          Rank 2                   Difference Error
A              5               8                              -3      9
B              10              7                               3      9
C              12              10                              2      4
D              4               1                               3      9
E              9               12                             -3      9
F              1               2                              -1      1
G              3               4                              -1      1
H              7               6                               1      1
I             2               5                              -3      9
J             11              9                               2      4
K              8               11                             -3      9
L             6               3                               3      9
SUM                   0    74

Coefficient: 0.741259

Equation       "=1-((6*F16)/(12*((12^2)-1)))"

How reliable does this scheme seem?

This scheme seems reliable as using Spearman's
coefficient proves there to be a positive correlation
between the separate rankings.
MATH 205 Lab#3 Q4                                                Name:                   PETER ABELS 201002080

Students       Programs           Reputation   Scholarship        Tuition
1900            15                  7.5        \$2,031           \$2,200
2200            16                   8         \$2,470           \$2,325
3010            18                  8.2        \$3,569           \$2,570
4230            19                  8.5        \$4,003           \$2,803
4000            19                  7.9        \$3,900           \$3,048
3987            19                 6.87        \$3,800           \$3,298
3800            20               6.1253        \$3,900           \$3,623
3763            23                  6.4        \$3,770           \$3,898

Students   Programs   Reputation Scholarship Tuition
Students                 1
Programs        0.77157411           1
Reputation      -0.2098597 -0.54468373           1
Scholarship     0.96396319 0.79355841 -0.1907239             1
Tuition         0.73545405   0.9378192 -0.7668886 0.72865587        1

Any effect on enrollment by increasing the number of programs offered at university?
Yes there is. By increasing the number of programs offered at the university, the
enrollment will rise as evident by the positive correlation (0.77157411)

Any effect on tuition by increasing the number of programs offered at the university?
Yes there is. By increasing the number of programs at the university, the tuition will
rise (due to factors like professors salaries, maintenance, etc.) There is a positive
correlation of 0.73545405

Does the level of scholarship have any effect on the enrollment?
Yes the level of scholarship does have an effect on enrollment. The is a very strong
postivie correlation between scholarship and enrollment (0.96396319). The more
scholarships the university offers the higher the enrollment and vice versa.

Is reputation related to anything?
Yes, according to the data provided reputation is negatively related tution.
However this is far from the truth as reputation plays a large role in the university
decision making process.

Programs                    30                      Regression Statistics
Reputation                   8                   Multiple R    0.98295725
Scholarship               4000                   R Square      0.96620496
Tutiton                   8500                                 0.92114492
Standard Error249.259318
Observations             8

Expected Enrollment:                16153.8667
=       16154 approximately

Assuming that enrollment would be equal is zero is none of the variables
existed, the expected enrollment with the given variables (programs,
reputation, scholarship, tuition) is 16154 approximately.

SUMMARY OUTPUT

16153.8667

ANOVA
df                SS         MS          F         Significance F
Regression                     4    5328934.88 1332233.72 21.4426085 0.0152
Residual                       3    186390.623 62130.2076
Total                          7     5515325.5

Coefficients Standard Error         t Stat         P-value Lower 95%Upper 95% Lower 95.0% Upper 95.0%
Intercept       -6955.7449 4214.74383            -1.6503363      0.19743845 -20369    6457.451 -20368.941    6457.451
Programs        -364.80684 216.631929            -1.6839939      0.19077146 -1054 324.612639 -1054.2263 324.612639
Reputation      879.492835 530.665352            1.65733985      0.19602976 -809.3 2568.30682 -809.32115 2568.30682
Scholarship     0.55522664 0.40803617            1.36072898      0.26680536 -0.743 1.85377983 -0.7433266 1.85377983
Tuition         2.91729032      1.6273542        1.79265848      0.17093264 -2.262 8.09625769 -2.2616771 8.09625769

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