The “Hotdog” excel file contains information on Alba (hotdog company) market sha
ID: 3223866 • Letter: T
Question
The “Hotdog” excel file contains information on Alba (hotdog company) market share as well as the information about their prices and the competition prices.
a) Run the regression estimating the effect of ALL prices on the market share of Alba company. Interpret the coefficient estimates (please copy and paste the table from Excel into this work file before interpreting the coefficients).
b) Did the signs of the coefficients match your expectations? Did the significance of the estimated coefficients matched your expectations? Discuss.
c) Test the hypothesis that Ball Park’s hotdog prices have no effect on Alba’s market share (hint: you will be testing joint hypothesis for Ball Park regular hotdogs and Ball Park All Beef hotdogs jointly not having statistically significant coefficients).
d) Discuss the possibility of Multicollinearity issue (hint! Most likely multicollinearity is present, think where and why!). Test for suspected multicollinearity and suggest the ways for dealing with it.
MKTALBA palba poscar pballparkreg pballparkbeef 0.045456499 149 169 169 179 0.093014501 149 199 189 199 0.059665602 189 199 189 199 0.0345966 189 199 189 199 0.027653599 189 169 159 169 0.029422401 189 199 189 199 0.036883201 189 199 189 199 0.041336901 189 189 189 199 0.0291296 189 189 169 179 0.039163899 189 189 189 199 0.033574101 189 189 189 199 0.034527499 189 179 189 199 0.041544098 189 189 189 199 0.0354724 189 189 189 199 0.037291098 189 179 189 199 0.0387742 189 189 189 199 0.0346312 179 189 179 189 0.0308691 179 189 189 199 0.030623101 179 189 189 199 0.0357931 179 159 189 199 0.034115601 179 189 189 199 0.029158801 179 189 189 199 0.0303488 179 189 189 199 0.034320898 179 189 189 199 0.0604463 148 168 178 188 0.035579 148 168 178 188 0.038465299 148 168 159 169 0.048557799 148 168 159 169 0.039835401 148 168 159 169 0.0497871 148 168 159 169 0.0577287 148 168 178 188 0.031367 148 168 159 169 0.0489478 148 168 159 169 0.047501199 148 168 178 188 0.0366625 148 168 149 159 0.041130699 148 168 149 159 0.048752401 148 168 178 188 0.0313043 148 168 149 159 0.0225279 169 159 149 159 0.030745899 169 159 149 159 0.029246399 169 179 149 149 0.021322301 159 159 149 149 0.0285528 159 159 149 149 0.025172601 169 179 179 189 0.087335303 159 179 179 189 0.054421298 159 159 179 189 0.022983 159 149 149 159 0.0287246 159 149 149 159 0.0304095 169 179 159 169 0.0271331 169 169 159 169 0.0195262 169 169 159 169 0.046467599 149 179 159 169 0.034252301 149 149 159 169 0.0235884 169 149 159 169 0.0223484 169 179 159 169 0.0170945 169 149 159 169 0.040803 159 149 159 169 0.032777902 159 179 159 169 0.031713899 169 179 159 169 0.022460399 169 179 149 159 0.022438001 169 159 149 159 0.0291005 169 159 179 189 0.0308691 169 159 179 189 0.0603255 139 159 179 189 0.040035099 139 159 179 189 0.0241614 169 159 159 169 0.0257325 169 159 159 169 0.0313356 169 159 179 189 0.039995 159 179 159 169 0.026542701 159 179 159 169 0.065480702 150 179 159 169 0.0244286 169 159 179 189 0.0173182 169 159 159 169 0.0187231 178 179 159 169 0.022914199 178 169 179 189 0.036044501 169 169 169 179 0.024502 169 179 169 179 0.034423999 169 169 179 189 0.024234001 169 169 159 169 0.0169413 178 179 159 169 0.034804799 169 169 159 169 0.0259392 169 169 179 189 0.028839801 178 169 179 189 0.019254699 178 169 159 169 0.0170603 178 179 159 169 0.0485093 159 179 179 189 0.023306999 159 149 179 189 0.0145524 178 149 149 149 0.050237201 159 149 149 149 0.053024601 159 179 179 189 0.024872299 178 169 179 189 0.013926 178 169 149 149 0.0257583 149 129 149 149 0.031936701 149 129 149 149 0.022415601 178 179 149 149 0.021687901 178 149 149 149 0.056190901 159 149 179 189 0.0303791 159 159 159 169 0.0164735 178 159 159 169 0.0456843 159 179 179 189 0.0354724 159 149 179 189 0.0236356 159 149 139 149 0.049439799 159 149 139 149 0.032386899 159 179 169 169 0.0223708 179 179 169 169 0.0190631 179 179 159 159 0.035014302 159 179 159 159 0.0295994 159 179 169 169 0.0234708 179 179 169 169 0.025223 179 179 179 189 0.054421298 159 169 179 189 0.061790898 159 169 179 189 0.074795298 149 169 179 189Explanation / Answer
a) Run the regression estimating the effect of ALL prices on the market share of Alba company. Interpret the coefficient estimates (please copy and paste the table from Excel into this work file before interpreting the coefficients).
Solution:
Here, we have to run the regression model for the estimation of the effect of all prices on the market share of Alba Company. The required regression model is given as below:
Descriptive Statistics
Mean
Std. Deviation
N
MKTALBA
.0349
.01428
113
palba
166.7434
13.63804
113
poscar
170.4690
14.44514
113
pballparkreg
168.2478
14.52862
113
pballparkbeef
176.8319
16.13941
113
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
Durbin-Watson
1
.725a
.526
.509
.01001
1.777
a. Predictors: (Constant), pballparkbeef, palba, poscar, pballparkreg
b. Dependent Variable: MKTALBA
ANOVAb
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
.012
4
.003
30.002
.000a
Residual
.011
108
.000
Total
.023
112
a. Predictors: (Constant), pballparkbeef, palba, poscar, pballparkreg
b. Dependent Variable: MKTALBA
Coefficients
Standard Error
t Stat
P-value
Intercept
0.040302626
0.014122568
2.853775
0.00518
palba
-0.000759769
8.0916E-05
-9.38961
0.00000
poscar
0.000262226
8.42699E-05
3.11174
0.00238
pballparkreg
0.000347267
0.000331608
1.04722
0.297336
pballparkbeef
0.000102492
0.000293759
0.3489
0.727844
The coefficient for the variable palba is given as -0.001 which mean there is a negative relationship exists between the dependent variable market share and independent variable palba. The p-value for this regression coefficient is given as 0.00 which indicate that the given coefficient is statistically significant. Also, the coefficient for the variable poscar is statistically significant as the p-value for this variable is given as 0.002. The variables pballparkreq and pballparkbeef are not statistically significant as the p-values for these variables are greater than the level of significance or alpha value 0.05 or 5%.
b) Did the signs of the coefficients match your expectations? Did the significance of the estimated coefficients matched your expectations? Discuss.
Answer:
Yes, the signs of the coefficients match with our expectations as we expect the negative relationship between the palba and share price. All other relationships are positive in nature. Also, the significance of estimated coefficients matched our expectations because we do not expect the effect of the last two variables on the regression model for prediction of share prices of the Company.
c) Test the hypothesis that Ball Park’s hotdog prices have no effect on Alba’s market share (hint: you will be testing joint hypothesis for Ball Park regular hotdogs and Ball Park All Beef hotdogs jointly not having statistically significant coefficients).
Answer:
Here, we have to use ANOVA F test for checking the significance of the overall model. The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: There is no significant effect of the Ball Park’s hotdog prices on the Alba’s market share.
Alternative hypothesis: Ha: There is a significant effect of the ball Park’s hotdog prices on the Alba’s market share.
The test statistic value is given as F = 30.002 with the p-value as 0.00 which is less than the level of significance or alpha value 0.05, so we reject the null hypothesis that there is no any significant effect of the Ball Park’s hotdog prices on the Alba’s market share.
This means we conclude that there is sufficient evidence that there is a significant effect of the ball Park’s hotdog prices on the Alba’s market share.
d) Discuss the possibility of Multicollinearity issue (hint! Most likely multicollinearity is present, think where and why!). Test for suspected multicollinearity and suggest the ways for dealing with it.
Answer:
There is a multicollinearity issue exists in the given regression model. There is significant correlation or linear relationships exist between the predictors. We would not reject the chance of auto-correlations.
The correlation coefficients between the different variables are shown by a correlation matrix as below:
MKTALBA
palba
poscar
pballparkreg
MKTALBA
1
palba
-0.432933781
1
poscar
0.169520668
0.48442813
1
pballparkreg
0.351738963
0.359283709
0.54880882
1
pballparkbeef
0.369472912
0.322571301
0.53367518
0.979383736
From the above correlation matrix it is observed that there is considerable positive or strong positive linear relationships exist between the given independent variables. These types of relationships are not good for the prediction of dependent variables.
Descriptive Statistics
Mean
Std. Deviation
N
MKTALBA
.0349
.01428
113
palba
166.7434
13.63804
113
poscar
170.4690
14.44514
113
pballparkreg
168.2478
14.52862
113
pballparkbeef
176.8319
16.13941
113
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