Business Startup Costs and Regression Analysis

This assignment delves into the analysis of business startup costs. It begins by calculating descriptive statistics like mean, median, and standard deviation to understand the central tendency and dispersion of the data. The non-normal distribution of startup costs is confirmed using frequency tables and histograms. One-way ANOVA is employed to compare the average startup costs across different businesses, demonstrating statistically significant variations. Furthermore, a regression model is developed using MS Excel to predict startup costs based on various independent variables. The model exhibits high explanatory power (R-squared = 0.9932) and statistical significance, with individual slope coefficients being significant at a 95% confidence interval. The assignment concludes by applying the regression equation to estimate annual sales.

STATISTICS
Student Id
[Pick the date]

TASK 1
1) Requisite descriptive statistics in relation to central tendency and dispersion of the data re
highlighted below.
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2) A) Tables(Frequency Distribution)
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B) Histograms (Startup Costs)
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3) The noteworthy observations based on the above analysis are as highlighted below.
 Non-normal probability distribution in relation to the startup costs.
Proof: i) For the various variables, there is no coincidence observed in the measures of central
tendency which should ideally happen.
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ii) For the various variables, the histograms drawn indicating the start-up costs are non-
symmetric.
 The startup costs required for different businesses tend to differ and are not the same.
Proof: i) The central tendency measures of startup costs across businesses do not coincide.
ii) The underlying patterns highlighted in the histograms of startup costs are different based on
the given sample data.
4)
The output for single factor ANOVA is outlined below which is preferred over T test for
comparing the means since there are a number of variables.
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In line with the output highlighted above, the p value (significance F) tends to be less than the
corresponding level of significance (0.05). This would result in rejection of null hypothesis and
consequent conclusion that the average startup costs tend to show variation across different
businesses.
TASK 2
1) Regression Output (MS-Excel Software)
Equation (Regression model)
2) It is apparent that coefficient of determination has a value equal to 0.9932.
Hence, the independent variables deployed in the regression model tend to have high explanatory
power which is why these tend to account for 99.32% of the changes in the dependent variable.
Thus, it would be appropriate to label the above regression model as having a good fit.
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3) Hypothesis Testing
ANOVA output pricked from the regression output is summarised below.
In line with the output highlighted above, the p value (significance F) tends to be less than the
corresponding level of significance (0.05). This would result in rejection of null hypothesis and
consequent conclusion that the regression model is significance owing to the slope being
significant.
4) The slopes of the various independent variables (i.e. X2, X3, X4, X5 & 6) can be interpreted
in the manner summarised below.
5) Confidence interval table
The above confidence interval implies that there is a 95% chance that the respective slope
coefficients would be found in the defined interval.
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6) Hypothesis Testing
For the slope coefficients, the p value has been identified, hence the following table can be used
to carry out the hypothesis testing based on the p value.
7) Considering that the respective slopes of all independent variables considered in the
regression model have proved their significance, hence the original model would see no
changes and would be the same.
8) The regression equation has been used from the earlier section and respective values have
been inserted to yield the annual sales below.
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