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5 7 7 Year (t) Year (t) Plot (i) "hat type of pattern exists in the data? Trend Pattern se simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. required, round your answers to two decimal places. 00 2.

5 7 7 Year (t) Year (t) Plot (i) "hat type of pattern exists in the data? Trend Pattern se simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. required, round your answers to two decimal places. 00 2.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Find the MSE in part (b) please.

### Linear Regression Analysis on Time Series Data #### Graph Description The graph on the left represents a time series data plot labeled “Year (t)” on the x-axis from 1 to 8, with the y-axis depicting an unspecified variable from 0 to 20. The data exhibits a trend pattern, indicating linear growth over time. #### Analysis **(b) Simple Linear Regression Analysis** - **Objective**: To find the parameters for the line that minimizes the Mean Squared Error (MSE) for the given time series. - **Results**: - **Y-intercept (b₀)**: 19.99 ✓ - **Slope (b₁)**: 1.77 ✓ - **MSE**: 2.94 ✗ (This answer appears incorrect based on feedback) **(c) Average Cost Increase** - **Question**: What is the average cost increase that the firm has been realizing each year? - **Result**: $1.77 ✓ **(d) Estimate of Cost/Unit for Next Year** - **Objective**: Compute an estimate of the cost per unit for the next year based on the linear regression model. - **Result**: $35.96 ✓ ### Feedback The overall attempt is marked as "Partially Correct," indicating some discrepancies in calculations, specifically regarding the MSE.
Transcribed Image Text:### Linear Regression Analysis on Time Series Data #### Graph Description The graph on the left represents a time series data plot labeled “Year (t)” on the x-axis from 1 to 8, with the y-axis depicting an unspecified variable from 0 to 20. The data exhibits a trend pattern, indicating linear growth over time. #### Analysis **(b) Simple Linear Regression Analysis** - **Objective**: To find the parameters for the line that minimizes the Mean Squared Error (MSE) for the given time series. - **Results**: - **Y-intercept (b₀)**: 19.99 ✓ - **Slope (b₁)**: 1.77 ✓ - **MSE**: 2.94 ✗ (This answer appears incorrect based on feedback) **(c) Average Cost Increase** - **Question**: What is the average cost increase that the firm has been realizing each year? - **Result**: $1.77 ✓ **(d) Estimate of Cost/Unit for Next Year** - **Objective**: Compute an estimate of the cost per unit for the next year based on the linear regression model. - **Result**: $35.96 ✓ ### Feedback The overall attempt is marked as "Partially Correct," indicating some discrepancies in calculations, specifically regarding the MSE.
The president of a small manufacturing firm is concerned about the continual increase in manufacturing costs over the past several years. The following figures provide a time series of the cost per unit for the firm's leading product over the past eight years. ### Data Table | Year | Cost/Unit ($) | |------|---------------| | 1 | 20.00 | | 2 | 24.50 | | 3 | 28.20 | | 4 | 27.50 | | 5 | 26.60 | | 6 | 30.00 | | 7 | 31.00 | | 8 | 36.00 | ### (a) Choose the correct time series plot. #### Graphs: 1. **Graph (i)**: - Displays an increasing trend in costs over the years. - Steadily rises from year 1 to year 8, consistent with the data table. 2. **Graph (ii)**: - Shows a similar rising trend but displays a slight dip between years 3 and 5, followed by an increase. 3. **Graph (iii)**: - Illustrates a decreasing trend, which contradicts the data table. 4. **Graph (iv)**: - Depicts a fluctuating downward trend with some decreases in the later years, which does not align with the data. The correct plot choice is "Graph (i)" as it accurately represents the increasing trend described in the data table.
Transcribed Image Text:The president of a small manufacturing firm is concerned about the continual increase in manufacturing costs over the past several years. The following figures provide a time series of the cost per unit for the firm's leading product over the past eight years. ### Data Table | Year | Cost/Unit ($) | |------|---------------| | 1 | 20.00 | | 2 | 24.50 | | 3 | 28.20 | | 4 | 27.50 | | 5 | 26.60 | | 6 | 30.00 | | 7 | 31.00 | | 8 | 36.00 | ### (a) Choose the correct time series plot. #### Graphs: 1. **Graph (i)**: - Displays an increasing trend in costs over the years. - Steadily rises from year 1 to year 8, consistent with the data table. 2. **Graph (ii)**: - Shows a similar rising trend but displays a slight dip between years 3 and 5, followed by an increase. 3. **Graph (iii)**: - Illustrates a decreasing trend, which contradicts the data table. 4. **Graph (iv)**: - Depicts a fluctuating downward trend with some decreases in the later years, which does not align with the data. The correct plot choice is "Graph (i)" as it accurately represents the increasing trend described in the data table.
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