Analysis of Startup Costs and Regression for Business Sales

This assignment focuses on the statistical evaluation of business startup costs and their impact on annual sales using various statistical tools such as frequency distributions, relative frequency histograms, and hypothesis testing with ANOVA. It observes that startup costs do not follow a normal distribution based on skewness and median-matching criteria. The analysis includes regression modeling to predict annual sales, demonstrating high model fit indicated by an R2 value of 0.9932, and significant predictor variables confirmed via p-values. Through hypothesis testing and ANOVA, the assignment concludes that startup costs vary significantly across different businesses.

STATISTICS
Student Name and Number
[Pick the date]
Task 1
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(1) The requisite computations are outlined below. It is noteworthy that all the figures
highlighted are in ($ 000’s).
(2) (a) The relevant frequency distribution for the variables of interest is outlined below.
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(b) The relative frequency histogram as required as pasted below.
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(3) Some key observations are outlined below.
 The startup costs for the various businesses do not adhere to a normal distribution.
This is apparent from multiple indicators such as skew being non-zero and also the
non-coincidence of mean and median.
 Further, from the relative frequency histogram, it becomes apparent that the setup
costs are greater than $30,000 for all the businesses except the pet shop.
(4) Hypothesis testing
ANOVA Single factor test
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Significance level (alpha) = 5%
Value of F statistics = 3.25 and the p value = 0.02
Conclusion:
It can be seen that the corresponding p value is not lower than alpha and thus, reject null
hypothesis and accept alternative hypothesis. Therefore, it can be claimed that for different
businesses, the startup costs are quite different.
TASK 2
(1) Excel Output
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Regression equation is highlighted below.
(2) The key consideration for determining the model fit would be the extent to which the
dependent variable (in this case annual sales) can be accounted for by the predictor
variables. This is clearly exceptionally high as R2 is 0.9932. Hence, the good fit is
confirmed.
(3) The hypotheses for testing are outlined below.
The applicable regression output from excel has been pasted below.
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The above output leads to p-value indicated by significance F as 0.000.
Decision: Null Hypothesis Rejection (Reason: p value exceeds α)
Conclusion: One of the dependent variables is significant.
(4) The relevant explanation of slope coefficients is summarized in the table.
(5) The confidence interval limits for the various variables are highlighted below.
(6) The testing of the individual slopes can be carried out as follows.
The table highlights the relevant output in relation of hypothesis testing..
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(7) The above table indicates that model does not need any change as the variables have
proved their significance based on hypothesis testing.
(8) The regression model to be used is captured by the following equation.
Based on the given values of the various input variables, we get the following.
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