Statistics Assignment: Task 1 & 2 - Hypothesis Testing & Regression

This statistics assignment presents an analysis of data using Excel, encompassing two main tasks. Task 1 involves calculating descriptive statistics such as mean, median, mode, and variance, and performing an ANOVA test to compare average startup costs across businesses. The assignment provides tables, frequency distributions, and identifies the skewness in startup costs. Task 2 focuses on regression analysis, presenting an equation derived from Excel output, evaluating the model's fit using R2 values, and conducting hypothesis testing for the regression coefficients. The assignment includes significance tests, confidence intervals, and a conclusion on the significance of independent variables, demonstrating a comprehensive approach to statistical analysis and modeling.

STATISTICS
TASK 1 & 2
STUDENT ID
[Pick the date]

Task 1
1. Through the use of the following functions in excel, requisite computations have been
performed on the given data.
Mean = Average ()
Median = Median ()
Mode = Mode ()
Variance = Var ()
Standard deviation = STDEV ()
Range = Max () – Min()
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2. (a) Requisite tables are illustrated below for each variable.
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(b) Relative frequency
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3) One key conclusion is with regards to the probability distribution to the startup costs which is
expected to be not normal considering missing symmetry. Thus, skew is present which also is
supported by the deviation between mean and median.
Also, by comparing the median value of startup costs coupled with the respective frequency
distribution histograms, differences are visible in terms of startup costs found across businesses.
4) H0: Across businesses, average startup costs does not significantly vary
Hi: Across businesses, average startup does show significant variation.
Realizing the presence of five variables for comparison, the correct choice would be ANOVA.
Excel Output – ANOVA
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Since F computed value does exceed the corresponding critical value, hence rejection of null
hypothesis framed. This hints at the difference between the mean average costs for businesses
being significant.
TASK 2
1) Excel output for regression
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The equation derived from excel output is illustrated as follows..
2) The regression model at hand represents a good fit primarily deciphered from R2 value which
comes out exceptionally high thereby indicating the ability of the predictors used in the model
to highlight the potential changes in the net annual sales (acting as the independent variable).
3) The hypothesis testing would essentially commence with listing down of the hypothesis.
H0: β = zero for X2, X3, X4, X5 & X6
H1: β ≠ zero for atelast either of one predictors
Observation: Significance F = 0.0000
Decision: Ho rejection
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Conclusion: Regression model is significant as for certain variables the zero slope assumption is
proved wrong.
4) Table for slope interpretation
5) Table for 95% confidence interval
6) The hypothesis testing would essentially commence with listing down of the hypothesis.
The hypothesis testing summary in terms of requisite p value is loaded as follows.
Since p value for all given variables is lower than corresponding significance level, hence
rejection of null hypothesis establishes significance of all independent variables.
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7) Since the above hypothesis test hints at the significance of all independent variables, hence a
better model cannot be obtained by deleting any parameter.
8) Putting the input set of values in the regression model deriving in (1), we get
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