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Assignment question answer sample of STAT7101 - Applied Statistics in Data Science

Q.1 A dataset contains the monthly sales (in AUD) of a company over the past five years. Use descriptive statistics to summarize the data and identify key trends. Provide the mean, median, mode, range, variance, and standard deviation. Additionally, visualize the data using a histogram and comment on its distribution.

Q.2 You are conducting a hypothesis test to evaluate whether the average time spent on a website by Australian users exceeds 15 minutes. The sample mean is 16.2 minutes with a standard deviation of 2.5 minutes (n = 50). Perform a one-sample t-test at a 5% significance level. State the null hypothesis, alternative hypothesis, and the test result.

Q.3 You are tasked with creating a regression model to predict house prices in Sydney based on factors such as square footage, number of bedrooms, and proximity to the CBD. Describe the steps to build the model, perform variable selection, and assess model performance.

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Statistics Assignment Sample

Q1:

Answer :

Q.1 Ans. : Mean: Calculate the average sales by summing all data points and dividing by the number of observations.
Median: The middle value when data points are arranged in ascending order.

  • Mode: The sales figure(s) that appears most frequently.
  • Range: Difference between the maximum and minimum sales figures.
  • Variance: Use the formula σ2=∑(xi−xˉ)2n\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n}σ2=n∑(xi​−xˉ)2​.
  • Standard Deviation: Square root of the variance.
  • Visualization: Generate a histogram using software like Python or R and interpret whether the data is normally distributed, skewed, or multimodal.

Q1:

Answer :

Q.2 Answer: Null Hypothesis (H₀): The average time spent on the website is 15 minutes (μ=15\mu = 15μ=15).
Alternative Hypothesis (H₁): The average time spent on the website exceeds 15 minutes (μ>15\mu > 15μ>15).

  • Test Statistic Formula: t=xˉ−μs/nt = \frac{\bar{x} - \mu}{s / \sqrt{n}}t=s/n​xˉ−μ​.
  • Calculation: Substitute xˉ=16.2,μ=15,s=2.5,n=50\bar{x} = 16.2, \mu = 15, s = 2.5, n = 50xˉ=16.2,μ=15,s=2.5,n=50.
  • Result: Compare the calculated t-value with the critical value for 49 degrees of freedom. Conclude whether to reject or fail to reject H0H₀H0​.

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Answer :

Q.3 Answer:  Data Preparation: Clean the data (handle missing values and outliers).
Exploratory Analysis: Use scatterplots and correlation coefficients to explore relationships.

  • Model Building: Fit a multiple linear regression model using the formula Y=β0+β1X1+β2X2+⋯+ϵY = \beta_0 + \beta_1X_1 + \beta_2X_2 + \dots + \epsilonY=β0​+β1​X1​+β2​X2​+⋯+ϵ.
  • Variable Selection: Use stepwise regression, LASSO, or backward elimination to identify significant predictors.
  • Model Performance: Evaluate using R-squared, adjusted R-squared, and RMSE (Root Mean Square Error).
  • Validation: Split the data into training and testing sets to assess predictive accuracy.