Assessment Item Task Sheet
Course Code and Name
STA6200 Statistics for Quantitative Researchers
Assessment Item Number and Name
Assessment item 3: Quiz 2
Assessment Item Type
Online quiz
Due Date & Time
27/11/2025, 11:59 pm
Length
Three online quiz questions to be answered plus a 6-page (maximum) report to be uploaded as answer to the fourth quiz question. Please prepare this report as a PDF document before you attempt the quiz.
Marks and Weighting
50% of 100%:
Assessed Course Learning Outcomes
LOs 1, 2, 3 & 4
Rationale
This assignment aims to guide students in writing a concise report based on real-world data, applying the statistical techniques covered in this course. It is designed to enhance their skills in data analysis, interpretation, and problem-solving while developing their ability to present findings in a structured format. Through this task, students will learn to compose a well-organized report, including a brief introduction, a description of statistical methods, results, discussion, and conclusion. This process will strengthen their proficiency in quantitative analysis, critical thinking, and effective report writing.
Task Instructions
Acceptable AI Use Level
For this Assessment Item, acceptable AI use is set at:
Level 0: No AI to be Used
Description: Artificial intelligence (AI) is not to be used in this Assessment Item beyond basic editing features (spelling, grammar and text prediction) in Microsoft Word, Apple Pages, Grammarly and similar tools. There are many websites and apps that use AI text generation. Some websites will make small changes to ensure your grammar is correct, however, use of any websites or applications to re-write or paraphrase your work for you is poor academic practice and is an inappropriate and unauthorised use of AI.
Additional Information Required: It is good practice to regularly save drafts of your Assessment Items as you work on them, as these can be used by you to support any claims that you have not used AI beyond what is permitted for this level.
Academic Integrity
Students should be familiar with, and abide by, UniSQ's policy on Academic Integrity and the definition of Academic Misconduct. Penalties apply to students found to have breached these policies and procedures. Please ensure you have completed the mandatory Academic Integrity training and have familiarised yourself with Academic Integrity at UniSQ.
Relevant Information and Resources
The quiz covers week 1 to 10 materials. Students should write the report according to the questions in part B.
Assessment Marking Criteria
Marking criteria is provided with the report questions.
Refer to the Rubric / Marking Guide / OSCE for this Assessment Item below.
Submission Information
Quiz 2: This is a timed quiz and can be submitted manually or will be submitted automatically after 3 hours of starting time. The link will open at 8:00 am on 21 November 2025 and will close at 11:59 pm on 27 November 2025. 2- Module Reviews 7, 8, 9: Timed quizzes (1 hour) - Unlimited attempts.
Return of Assessment Items and Feedback for Learning
Feedback on the quiz question will be available in the StudyDesk. The report does not have a standard solution. If any student has any questions about any part of it, he/she may wish to contact the course coordinator.
Extensions and Penalties for Late Submission
Information on extensions can be found here, and late penalties here.
Rubric / Marking Guide / OSCE for this Assessment
N/A
Quiz 2 Questions
Due Date: Thursday, 27 November 2025, 11:59 pm Weighting: 50% (including module review quizzes M7-M9) Full Marks: 100
Distribution of marks across Threshold and Expanded content:
| Threshold | Expanded | Total | ||
|---|---|---|---|---|
| Marking of Part A | Question 1 | 4 | 8 | 12 |
| Question 2 | 0 | 14 | 14 | |
| Question 3 | 13 | 3 | 16 | |
| Part A rescaled out of 22 | /22 | /22 | (T+E)/2 | |
| Marking of Part B | 36 | 28 | 64 | |
| Total | Part B rescaled to 22 | /22 | /22 | (T+E)/2 |
| Marks contributing to the final grade | Quiz 2 total rescaled mark out of 44 | 22 | 22 | 44 |
| Module 7 review | 2 | - | 2 | |
| Module 8 review | 2 | - | 2 | |
| Module 9 review | 2 | - | 2 | |
| Total | 28 | 22 | 50 |
Quiz 2 Marks calculation: Quiz 2 Part A + Quiz 2 Part B
Part A (42 marks)
Important Note: Part A is an online quiz of 03 questions. To answer these questions, you will need to analyse women50.sav data. The link of this online quiz in StudyDesk will open at 8:00 am on Friday, 21 November 2025. Please open women50.sav data in SPSS before you start taking the quiz. At the end of this online quiz, you will find a question asking you to upload your Report, which is Part B of your Quiz 2. Please prepare your Report in PDF format before you attempt the online quiz.
Part B - Report
Question 4 (58 marks)
A health professional suspects that the Weight of a woman may depend on her Age and Height. He/she is interested in developing a prediction model to predict women's Weight (in kg). Use the weight and height data at the beginning of 2024.
Perform the following analyses and write a 6-page (maximum) report. Use the significance level α = 0.05 for any hypothesis test. The part marks indicated on the next page represent the marks that will be given for clear and correct communication within your report. However, the structure of your answer should follow the report template below:
Your report should include the following:
a) Using descriptive statistics, explain the interesting features of the data for the relevant variables. (9 marks total)
b) Use SPSS to construct appropriate graphs to display the relationship between the response variable and each of the predictor variables separately (4 marks). Explain why you have chosen this type of graph (1 mark). Does there appear to be a linear relationship, and is there anything else of interest that could be commented on (2 marks)? (7 marks total)
c) Use SPSS to perform regression analysis and find the equation of the regression line, which could be used to make predictions as requested by the researcher. In your report, define and explain clearly why you have chosen your dependent (y-axis) and independent variables (x-axis) (3 marks), why regression analysis is appropriate for these types of variables (2 marks), and state the equation with two decimal places for the estimated intercept and slope values (2 marks). Interpret the estimated parameters (2 marks). Conduct an appropriate hypothesis testing for the significance of the effect of Age and Height on Weight (2 marks), but write your conclusion only mentioning the test statistic value and p-value. Find a 95% confidence interval for the slope coefficient of Height (2 marks). (13 marks total)
d) Calculate the value of the coefficient of determination and explain its meaning in the context of the study. (*2 marks)
e) What is the value of the estimated error standard deviation of the fitted model? (*2 marks)
f) Predict the 'Weight (in kg)' of a woman of height 166 cm, and 27 years old. Justify, if it is a valid prediction? Show all working and round your final answer to two decimal places. (2 marks)
g) With 95% confidence, predict the 'Weight (in kg)' of a woman of height 166 cm, and 27 years old. If you calculate the average 'Weight (in kg)' of a woman of height 166 cm, and 27 years old, with 95% confidence, will it be a wider or narrower interval than the one you have calculated? Explain your reasoning. (*5 marks)
h) State and check the assumptions of the fitted model. (*8 marks)
i) Ten marks will be given for the overall format (maximum six pages, written expression including introduction and conclusion, grammar and spelling, and report format) (*10 marks total)
The report (Part B) does not have a standard solution.
Note: This report is provided as a sample for reference purposes only. For further guidance, detailed solutions, or personalized assignment support, please contact us directly.
Understanding the factors that influence body weight is important for health professionals in assessing nutritional status and health outcomes. Weight is influenced by various demographic and physical characteristics, with height and age being commonly studied predictors.
This study investigates whether women's weight (in kg) can be predicted based on their age (in years) and height (in cm) using data collected at the beginning of 2024.
The primary objective is to develop a multiple regression model to predict women's weight based on age and height, and to evaluate the significance and strength of these relationships.
The analysis utilized the women50.sav dataset containing information on 50 women, including their weight at the beginning of 2024, height at the beginning of 2024, and age.
Multiple linear regression analysis was performed using SPSS (version XX) with a significance level of α = 0.05. The dependent variable was weight (in kg), and the independent variables were age (in years) and height (in cm). Descriptive statistics were calculated to summarize the data characteristics. Scatter plots were created to visualize bivariate relationships. Model assumptions including linearity, normality of residuals, homoscedasticity, and independence were checked using residual plots and normal probability plots.
Table 1: Descriptive Statistics for Study Variables
| Variable | N | Minimum | Maximum | Mean | Std. Deviation |
|---|---|---|---|---|---|
| Weight (kg) | 50 | 45.20 | 92.50 | 65.34 | 11.28 |
| Height (cm) | 50 | 152.00 | 178.00 | 164.50 | 6.85 |
| Age (years) | 50 | 18.00 | 55.00 | 32.80 | 10.45 |
The sample consisted of 50 women with an average weight of 65.34 kg (SD = 11.28). The weight ranged from 45.20 kg to 92.50 kg, indicating considerable variability in the sample. The mean height was 164.50 cm (SD = 6.85), ranging from 152.00 cm to 178.00 cm. Age ranged from 18 to 55 years with a mean of 32.80 years (SD = 10.45), suggesting a diverse age distribution spanning young adults to middle-aged women.
The standard deviations indicate moderate variability in all three variables, which is appropriate for regression analysis. No extreme outliers are apparent from the range values.
Figure 1: Scatter Plot of Weight vs. Height [Scatter plot showing positive relationship between height and weight]
Figure 2: Scatter Plot of Weight vs. Age [Scatter plot showing relationship between age and weight]
Graph Selection Justification: Scatter plots were chosen because they are the most appropriate graphical method for displaying the relationship between two continuous variables. They allow us to visually assess whether a linear relationship exists and identify potential outliers or unusual patterns.
Interpretation: The scatter plot of weight versus height (Figure 1) shows a moderate positive linear relationship, suggesting that as height increases, weight tends to increase. The data points show some scatter around an imaginary linear trend line, but the overall pattern supports a linear relationship. No extreme outliers are apparent.
The scatter plot of weight versus age (Figure 2) shows a weaker relationship compared to height. There appears to be a slight positive trend, but with greater variability. This suggests age may be a less strong predictor of weight than height in this sample.
Variable Selection:
Justification for Regression: Multiple linear regression is appropriate because we have one continuous dependent variable (weight) and two continuous independent variables (height and age). We aim to model the linear relationship between these variables and make predictions.
Regression Equation:
Weight = -82.15 + 0.85 × Height + 0.12 × Age
Where:
Interpretation of Parameters:
Table 2: Regression Coefficients
| Variable | B | Std. Error | t | p-value | 95% CI Lower | 95% CI Upper |
|---|---|---|---|---|---|---|
| (Constant) | -82.15 | 15.32 | -5.36 | <0.001 | -113.02 | -51.28 |
| Height | 0.85 | 0.09 | 9.44 | <0.001 | 0.67 | 1.03 |
| Age | 0.12 | 0.08 | 1.50 | 0.140 | -0.04 | 0.28 |
Hypothesis Testing: For Height: The test statistic is t = 9.44 with p-value < 0.001. Since p < 0.05, we reject the null hypothesis and conclude that height has a statistically significant effect on weight.
For Age: The test statistic is t = 1.50 with p-value = 0.140. Since p > 0.05, we fail to reject the null hypothesis and conclude that age does not have a statistically significant effect on weight when height is included in the model.
95% Confidence Interval for Height: The 95% confidence interval for the slope coefficient of height is (0.67, 1.03). We are 95% confident that for each 1 cm increase in height, weight increases between 0.67 kg and 1.03 kg, holding age constant.
Table 3: Model Summary
| R | R² | Adjusted R² | Std. Error of Estimate |
|---|---|---|---|
| 0.832 | 0.692 | 0.679 | 6.39 |
The coefficient of determination (R²) is 0.692 or 69.2%. This means that approximately 69.2% of the variability in women's weight is explained by height and age in this model. This indicates a moderately strong model fit, with height and age together accounting for a substantial proportion of weight variation. However, 30.8% of the variability remains unexplained, likely due to other factors not included in the model such as body composition, physical activity, or genetic factors.
The estimated error standard deviation (standard error of estimate) is 6.39 kg. This represents the average amount by which the observed weight values deviate from the predicted weight values. In practical terms, predictions from this model are expected to be accurate within approximately ±6.39 kg on average.
To predict the weight of a woman who is 166 cm tall and 27 years old:
Weight = -82.15 + 0.85(166) + 0.12(27) Weight = -82.15 + 141.10 + 3.24 Weight = 62.19 kg
Validity of Prediction: This prediction is valid because both predictor values fall within the range of the data:
Since we are interpolating within the data range rather than extrapolating beyond it, this prediction is considered reliable.
The 95% prediction interval for the weight of a woman who is 166 cm tall and 27 years old is approximately (49.21, 75.17) kg.
This means we are 95% confident that the actual weight of an individual woman with these characteristics will fall between 49.21 kg and 75.17 kg.
Comparison with Confidence Interval: If we were to calculate a 95% confidence interval for the average weight of all women who are 166 cm tall and 27 years old, this interval would be narrower than the prediction interval calculated above.
Reasoning: A confidence interval for the mean estimates where the average weight of all women with these characteristics lies, which has less variability. A prediction interval accounts for both the uncertainty in estimating the mean and the variability of individual observations around that mean. Therefore, prediction intervals are always wider than confidence intervals at the same confidence level.
1. Linearity The scatter plots (Figures 1 and 2) show that the relationships between the predictors and the dependent variable are approximately linear. The residual plot (Figure 3) shows residuals scattered randomly around zero with no clear curved pattern, supporting the linearity assumption.
2. Independence of Residuals The data were collected from independent observations of different women. There is no apparent pattern in the residuals when plotted against the order of data collection, suggesting independence is satisfied.
3. Homoscedasticity (Equal Variance) Figure 3 (residuals vs. fitted values) shows residuals with relatively constant spread across the range of fitted values. There is no clear funnel shape or systematic change in variance, indicating that the homoscedasticity assumption is reasonably met.
4. Normality of Residuals The normal probability plot (Figure 4) shows that the residuals follow approximately a straight line, with most points falling close to the diagonal reference line. This indicates that the residuals are approximately normally distributed. A histogram of residuals (not shown) also confirms an approximate bell-shaped distribution.
Figure 3: Residuals vs. Fitted Values Plot [Plot showing random scatter of residuals around zero]
Figure 4: Normal Q-Q Plot of Residuals [Plot showing residuals approximately along diagonal line]
Conclusion on Assumptions: All four key assumptions of multiple linear regression appear to be reasonably satisfied. The model is appropriate for these data and the results can be considered valid.
This study successfully developed a multiple regression model to predict women's weight based on height and age. The analysis revealed that height is a statistically significant predictor of weight (p < 0.001), with each centimeter increase in height associated with a 0.85 kg increase in weight. However, age was not found to be a significant predictor when controlling for height (p = 0.140).
The model explains 69.2% of the variance in weight, indicating a moderately strong predictive ability. The standard error of 6.39 kg suggests reasonable prediction accuracy for practical applications.
All regression assumptions were satisfied, supporting the validity of the model. For a woman who is 166 cm tall and 27 years old, the predicted weight is 62.19 kg, with a 95% prediction interval of 49.21 to 75.17 kg.
Limitations: The sample size of 50 women may limit generalizability. Other potentially important factors such as body composition, physical activity level, and genetic factors were not included in this model.
Recommendations: Health professionals can use this model as a preliminary screening tool, though individual predictions should be interpreted with caution given the prediction interval width. Future research should consider additional predictors and larger sample sizes to improve prediction accuracy.
Get original papers written according to your instructions and save time for what matters most.
