Question

In: Statistics and Probability

Run two regressions using Excel from the data below. Find the following information: 1. estimated regression...

Run two regressions using Excel from the data below. Find the following information: 1. estimated regression equations for both regressions 2. both coefficients of determination. 3. significance of each independent variable 4.Report the significance of both models. 5.Predict y for a fictitious set of x values for both

Years Weekend Daily Tour Income Daily Gross Revenue Number of Tourists
1 Friday 3378 4838.95 432
1 Saturday 1198 3487.78 139
1 Sunday 3630 4371.3 467
2 Friday 4550 6486.48 546
2 2467 3437.39 198
2 Sunday 3593 4571.43 452
3 Friday 898 2515.15 119
3 Saturday 2812 5462.11 342
3 Sunday 2650 5498.89 321
4 Friday 3230 5071.14 402
4 Saturday 4798 8051.43 523
4 Sunday 3253 4291.95 353
5 Friday 2848 4545 347
5 Saturday 4632 8865.01 534
5 Sunday 3767 4710.64 412
6 Friday 4499 10752.74 529
6 Saturday 3868 6435.63 422
6 Sunday 2489 3389.37 288
7 Friday 3448 6129.58 367
7 Saturday 3612 7357.12 406
7 Sunday 1937 2121.76 216
8 Friday 2548 4738.86 294
8 Saturday 2833 4141.98 317
8 Sunday 2214 4878.35 284
9 Friday 1520 4102.49 169
9 Saturday 4322 8639.55 462
9 Sunday 1833 3946.71 203
10 Friday 2271.63 4236.31 235
10 Saturday 2407.88 5613.27 266
10 Sunday 1772.17 5580.17 182
11 Friday 1494 3833.52 177
11 Saturday 1998 3986.57 213
11 Sunday 1388 2721.56 165
12 Friday 1925 3952.19 190
12 Saturday 2695 6281.3 243
12 Sunday 1525 3356.14 172
13 Friday 1725 3822.59 187
13 Saturday 2450 4141.75 253
13 Sunday 1407.5 3312.41 173
14 Friday 2394 4571.5 242
14 Saturday 3012 6363.3 311
14 Sunday 2058 3502.22 239
15 Friday 2427 5881.13 267
15 Saturday 3189 10409.13 336
15 Sunday 2109 4955.05 178
16 Friday 2244 4347.41 184
16 Saturday 3195 4935.17 274
16 Sunday 1017 3486.27 114
17 Friday 3470 6290.99 325
17 Saturday 5323 13132.55 478
17 Sunday 2345 5014.45 242
18 Friday 1671 2740.23 177
18 Saturday 2321.94 4423.31 246
18 Sunday 1542 2650.48 182

Solutions

Expert Solution

Analysis
regression 1:

1)  
regression equation:   
Daily Gross Revenue = 1408.52 + 12.68*number of tourists  
  
2)  
R^2 =    48.91%
  
3)  
Ho: beta1 is not significant  
h1: beta1 is significant  
With t=7.05, p<5%, I reject ho and conclude that beta1 is significant.  
  
4)  
Ho: model is not significant  
h1: model is significant  
With F=49.79, p<5%, I reject ho and conclude that the model is significant.

5)
when x= 119,
predicted Y = 1408.52 + 12.68*119 = 2917.44

regression 2:

1)  
regression equation:   
Daily Gross Revenue = 748.65179 + 1.6362*Daily Tour Income  
  
2)  
R^2 = 62.707%
  
3)  
Ho: beta1 is not significant  
h1: beta1 is significant  
With t=9.35, p<5%, I reject ho and conclude that beta1 is significant.  
  
4)  
Ho: model is not significant  
h1: model is significant  
With F=87.43, p<5%, I reject ho and conclude that the model is significant.

5)
when x= 3012,
predicted Y = 748.65179 + 1.6362*3012 = 5676.88619

procedure
data -> data analysis -> regression

regression 1: dependent variable: Daily Gross Revenue
independent variable: Number of Tourists

regression 2: dependent variable: Daily Gross Revenue
independent variable: Daily Tour Income

output
regression 1:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.699382402
R Square 0.489135744
Adjusted R Square 0.479311431
Standard Error 1543.231194
Observations 54
ANOVA
df SS MS F Significance F
Regression 1 118573929.8 1.19E+08 49.78829188 4.02752E-09
Residual 52 123841250.9 2381563
Total 53 242415180.7
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 1408.526138 566.125925 2.488009 0.016088648 272.5113593 2544.541 272.5114 2544.541
Number of Tourists 12.68245322 1.797378968 7.056082 4.02752E-09 9.075748453 16.28916 9.075748 16.28916

regression 2:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.791878228
R Square 0.627071127
Adjusted R Square 0.619899418
Standard Error 1318.533714
Observations 54
ANOVA
df SS MS F Significance F
Regression 1 152011560.6 1.52E+08 87.43677682 1.00186E-12
Residual 52 90403620.06 1738531
Total 53 242415180.7
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 748.6517999 500.552028 1.495652 0.140789091 -255.7793278 1753.083 -255.779 1753.083
Daily Tour Income 1.636240094 0.174984653 9.350763 1.00186E-12 1.285107699 1.987372 1.285108 1.987372

orchestra answered 2 years ago
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