Questions

MUF0142 Fund. Mathematics Unit 2 - Semester 1, 2025

Multiple fill-in-the-blank

Question textGuidelines to answer the following question:Answer the following questions by filling in the blanks. If the answer requires a number, enter the number only. Do not use any spaces or brackets. If you get an error message saying you need to complete this question, please check the format of all your answers. [Total: 2 + 3 + 2 = 7 marks] The table at the side shows the number of vehicles waiting at a railway crossing in a Melbourne suburb on 19 separate occasions during a particular day, and the length of time (in minutes) they waited for. The relationship between the number of vehicles and the time they waited is found to be non-linear. In order to linearise the data, a squared transformation is to be applied to the variable Time. a. Apply a squared transformation to the time variable and find the equation of the least squares regression line that predicts the number of vehicles based on Time2 , correct all coefficients to 4 decimal places. Number of vehicles = Answer 1 Question 8[input] + Answer 2 Question 8[input] × time2 b. Use your regression equation to predict the number of vehicles waiting after 6 minutes. Hence, find the residual. Number of vehicles = Answer 3 Question 8[input] + Answer 4 Question 8[input] × Answer 5 Question 8[input]2 Predicted number of vehicles is Answer 6 Question 8[input]. (Correct to the nearest whole number) Residual = Answer 7 Question 8[input] vehicles. c. i. Is the prediction in part b reliable? Answer 8 Question 8[select: , No, Yes] ii. Explain your answer using the following options: Answer 9 Question 8[select: , The prediction is an extrapolation outside the given range, The prediction is an interpolation within the range of data, The prediction is based on a measured data point] Please answer all parts of the question.

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Step-by-Step Analysis

We begin by understanding the task and the structure of the question. The problem asks us to (a) apply a squared transformation to Time and derive a least-squares regression line predicting Number of vehicles from Time^2, with coefficients to 4 decimal places; (b) use that regression to predict at 6 minutes, compute the residual, and report the predicted value and residual; (c) assess the reliability of the prediction and choose an explanation from provided options. Option 1: The constant term (intercept) of the regression is -4.2121. This value would appear in the regression equation as the intercept when predicting Number of vehicles from Time^2 if the data and calculation truly yield that intercept. Check for plausibility: with Time^2 being small near low times, the intercept is the baseline prediction when Time^2 = 0. A negative intercept implies the model would predict negative vehicles at Time^2 = 0, which could be unrealistic but not impossible if the line still fits well across the observed Time^2 values. If the computed regression line with a negative intercept and a positive slope yields reasonable predictions over the observed range, this ......Login to view full explanation

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