Question 1
y = (1/200)*x 1 + (1/255)*x 2 + 10*x 3 + 5*x 4 … Equation 1
Equation 1 can also be rewritten as:
According to the coefficients obtained from the regression model, which is provided below, the coefficients of x would now be the following:
… Equation 2
Thus, the equation needs to be updated because the coefficients of x have changed in the new equation.
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Question 2
The intercept is provided as -2.38 in this model, and represents the total time when all values of x=0. In the instance that this figure was a positive value, it would give the average time taken to produce when all factors of x (size change, label change and packing for 12oz and 24oz units) are equal to zero. But bringing this picture into this model, a positive value would still be insignificant, since when x=0, no production has been done.
Table 1 : Q1 Regression Results
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.965203425 |
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R Square |
0.931617652 |
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Adjusted R Square |
0.920676476 |
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Standard Error |
16.72998826 |
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Observations |
30 |
||||
|
ANOVA |
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|
df |
SS |
MS |
F |
Significance F |
|
|
Regression |
4 |
95328.98732 |
23832.24683 |
85.1478558 |
3.45722E-14 |
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Residual |
25 |
6997.312676 |
279.8925071 |
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|
Total |
29 |
102326.3 |
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Coefficients |
Standard Error |
t Stat |
P-value |
||
|
Intercept |
-2.377596872 |
16.29754833 |
-0.145886781 |
0.885180711 |
|
|
24oz units |
0.002241511 |
0.00102527 |
2.18626413 |
0.038370782 |
|
|
12oz units |
0.004702737 |
0.002013478 |
2.335628347 |
0.027832267 |
|
|
Size change |
14.20807705 |
1.983746946 |
7.16224268 |
1.66017E-07 |
|
|
Label change |
5.255946235 |
1.588585996 |
3.30856891 |
0.002844316 |
|
Case 2: Question 2 – 4
Question 2a.
From the data obtained, attractiveness would be expressed in this equation:
Where y is profit, a is the coefficient of profit and x 1 is the profit amount. P value for attractiveness is 0.0023, indicating that the null hypothesis that attractiveness is of no effect to profit can be rejected. With a high regression coefficient in the model above, it is recommended that continuously good looks for the hotel locations will result in increasing profits.
Table 2 : Q2a Regression Result
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.385195812 |
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R Square |
0.148375814 |
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|
Adjusted R Square |
0.133692638 |
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|
Standard Error |
244.2010126 |
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|
Observations |
60 |
||||
|
ANOVA |
|||||
|
df |
SS |
MS |
F |
Significance F |
|
|
Regression |
1 |
602612.3686 |
602612.3686 |
10.10515828 |
0.002372386 |
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Residual |
58 |
3458779.804 |
59634.13455 |
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|
Total |
59 |
4061392.172 |
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|
Coefficients |
Standard Error |
t Stat |
P-value |
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|
Intercept |
158.637516 |
91.66348334 |
1.730651184 |
0.08883159 |
|
|
Attract |
108.7188644 |
34.20057023 |
3.178861161 |
0.002372386 |
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Question 2b
In this model combining all factors, all factors except attractiveness post significant results that indicate that they have an effect on the profitability of the hotel venture. In this instance, the attractiveness of the hotel posts marginally significant results to indicate that attractiveness contributes to profitability, as opposed to the first model where there was strong significance. The first regression model gives more credible information about the effect of attractiveness, since it considers attractiveness as its own factor and avoids the confounding effect provided by the other factors. However, while considering the business environment as a whole, which this study has done, the second model provides a more wholesome view of the business situation.
Table 3 : Q2b Regression Result
|
SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.944026 |
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|
R Square |
0.891185 |
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|
Adjusted R Square |
0.88111 |
||||
|
Standard Error |
90.46589 |
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|
Observations |
60 |
||||
|
ANOVA |
|||||
|
df |
SS |
MS |
F |
Significance F |
|
|
Regression |
5 |
3619452 |
723890.4 |
88.45107107 |
9.35899E-25 |
|
Residual |
54 |
441940.2 |
8184.077 |
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|
Total |
59 |
4061392 |
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|
Coefficients |
Standard Error |
t Stat |
P-value |
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|
Intercept |
-548.648 |
58.79416 |
-9.33168 |
7.46218E-13 |
|
|
Size |
255.9772 |
26.09853 |
9.808107 |
1.35161E-13 |
|
|
Advertexp |
9.570961 |
1.033152 |
9.26385 |
9.53501E-13 |
|
|
Mgrperf |
91.36652 |
12.37958 |
7.380419 |
9.93413E-10 |
|
|
Neighbors |
19.65079 |
1.741969 |
11.28079 |
8.09143E-16 |
|
|
Attract |
-3.25107 |
14.50795 |
-0.22409 |
0.823533862 |
|
Question 3
Local advertising expenditure is regressed against profits to determine whether there is an effect when advertising expenditure increased. The significance value for the regression model is 0.0004, which indicates that there is a relationship. The coefficient for the advertising is positive, indicating that there is an increasing effect on profit when advertising expenditure is increased.
Table 4 : Q3 Regression Output
|
SUMMARY OUTPUT |
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|
Regression Statistics |
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|
Multiple R |
0.441674452 |
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|
R Square |
0.195076321 |
||||
|
Adjusted R Square |
0.181198327 |
||||
|
Standard Error |
237.4109898 |
||||
|
Observations |
60 |
||||
|
ANOVA |
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|
df |
SS |
MS |
F |
Significance F |
|
|
Regression |
1 |
792281.4446 |
792281.4446 |
14.05652106 |
0.000411248 |
|
Residual |
58 |
3269110.728 |
56363.97806 |
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|
Total |
59 |
4061392.172 |
|||
|
Coefficients |
Standard Error |
t Stat |
P-value |
||
|
Intercept |
124.696973 |
87.56959334 |
1.4239757 |
0.159811449 |
|
|
Advertexp |
9.869514065 |
2.632430091 |
3.749202723 |
0.000411248 |
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Question 4
Profit is regressed against manager performance rating to determine whether more talented managers could lead to higher profits at different hotel sites. According to the data, p-value of 0.0002 vacates the null hypothesis that there is no relationship between these two factors. The coefficient provided as 124.
|
SUMMARY OUTPUT |
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|
Regression Statistics |
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|
Multiple R |
0.458343 |
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|
R Square |
0.210078 |
||||
|
Adjusted R Square |
0.196459 |
||||
|
Standard Error |
235.1882 |
||||
|
Observations |
60 |
||||
|
ANOVA |
|||||
|
df |
SS |
MS |
F |
Significance F |
|
|
Regression |
1 |
853209.6 |
853209.6 |
15.42498 |
0.000231 |
|
Residual |
58 |
3208183 |
55313.49 |
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|
Total |
59 |
4061392 |
|||
|
Coefficients |
Standard Error |
t Stat |
P-value |
||
|
Intercept |
0.208631 |
114.1176 |
0.001828 |
0.998548 |
|
|
Mgrperf |
124.6264 |
31.73201 |
3.927465 |
0.000231 |
|
