Math Problem Statement

Questions 1 to 5 are based on the data in worksheet named "Problem 1".

The data shows the measured weekly fuel consumption in tons (dependent variable y) vs the average hourly temperature (independent variable x) in the past.

Plot the data. Remember to use a “scatter plot” (no need to submit the chart). value of R2 is 0.7633 for your best fit (do not use more than a third degree to avoid overfitting).

Create a second independent variable (x2: x-squared). Using the Regression function in Data Analysis of Excel, answer the following two questions:

(Remember in Excel the independent variables should all be next to each other to be able to run a multiple regression.)

What are the values of b0, b1 and b2, respectively?

Plot the data. Remember to use a scatter plot. The value of R2 is 0.7633 for your best fit. Create a second independent variable (x2: x-squared). Using the Regression function in Data Analysis of Excel, answer the following two questions: What are the values of b0, b1, and b2?

Solution

Here is the OCR-extracted data from the image, though some text has slight recognition errors. Let's reconstruct the table based on the extracted content:

Sample WeekAvg Hrly Temp (X1)Wkly Fuel Consump (Y)
128.012.4
228.011.7
332.512.4
443.013.2
545.99.4
658.89.5
758.18.0
862.57.5
975.07.9
1068.06.1
1165.04.0
1273.04.5
1373.06.4
1487.09.0
1595.010.0
1690.012.0
1787.010.2
1896.018.0
19105.022.0
2095.016.3
2180.014.0
2295.017.0
2397.015.0

Next, I will calculate X2=X12X_2 = X_1^2 and use Python to perform multiple linear regression to determine the coefficients b0b_0, b1b_1, and b2b_2.

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Math Problem Analysis

Mathematical Concepts

Statistics
Multiple Linear Regression
Quadratic Regression

Formulas

Y = b0 + b1*X1 + b2*X2

Theorems

Least Squares Regression

Suitable Grade Level

Undergraduate

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