Statistics Assignment: Regression Analysis and Hypothesis Testing

This statistics assignment delves into various statistical concepts. It begins by analyzing a frequency table and histogram, identifying the presence of positive skewness and discussing the implications for choosing the appropriate measure of central tendency (mean vs. median). The assignment then explores hypothesis testing using ANOVA, examining the relationship between unit price and demand, calculating the coefficient of determination and correlation, and interpreting the results. Further analysis involves another ANOVA test to determine if there is a significant difference between population means. Finally, the assignment concludes with regression analysis, including hypothesis testing for slope coefficients, interpreting the impact of mobile phone advertising spots on sales, and calculating predicted sales based on specific unit prices and advertising spots. The assignment provides comprehensive coverage of statistical techniques and their applications.

STATISTICS
ASSIGNMENT
Student Name
[Pick the date]

Question 1
a. Frequency table
b. Histogram
The histogram above clearly refers to the presence of positive skew due to which the shape of the
graph is asymmetric. This can be inferred from a right side tail which is present. Hence, it ca also
be concluded that the above distribution cannot be termed as normal distribution.
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c. Mean as an indicator of central tendency is used when the shape of the graph is symmetric
which implies that outliers are not present in the data. However, this is not the case here and
median would be a better choice considering that it is immune to distortion from extreme
values.
a. ‘Demand and unit price are related’
 Hypotheses
 ANOVA
 Value of test statistic
 Degree of freedom : df =47
 The p value: p=0.00
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 Level of significance ∝=0.05
 Since, p<∝ (0.00<0.05), thus reject null hypothesis
 Significant relation does exist between unit price and demand.
(b) The value of coefficient of determination
Correlation of determination( R¿¿ 2)¿
61.7% of deviation in ‘demand’ will be described by relevant deviations in ‘unit price.’
(c) The value of coefficient of correlation
The sign of coefficient of correlation would depend on the sign of independent variable slope
coefficient. Therefore, the negative sign of slope coefficient (unit price) implies that the
coefficient of correlation is negative (R=−0.786). price. This refers to the lower price beig
conducive to higher demand.
Question 3
 Hypotheses
 ANOVA
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 Value of F statistic
 Degree of freedom : df =23
 The p value: p=0.00
 Level of significance ∝=0.05
 Since, p<∝ (0.00<0.05), thus reject null hypothesis
 There exists at the minimum one population whose mean deviates significantly from others.
Question 4
 ANOVA
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a) The regression equation
b) Hypothesis Testing
 Value of F statistic
 The p value: p=0.00
 Level of significance ∝=0.05
 Since, p<∝ (0.00<0.05), thus reject null hypothesis
 “Significant relationship is present between at least one of the independent variables and
dependent variable.”
c) Hypothesis testing for slope coefficients
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(d) The x2 slope coefficient is indicative of the fact that the change in the mobile phone
advertising spots tends to bring about a change in the daily sales of mobile phone by 0.4733
units. The direction of change for these two variables is the same owing to positive value of the
slope coefficient.
(e) Number of mobile set sold for mobile unit price of $20,000 and 10 advertising spots.
Therefore, 9960 is the total number of mobile sets sold for mobile unit price of $20,000 and 10
advertising spots.
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