Math Problem Statement
Solution
Let's solve this step by step based on the image. Here's how we'll proceed:
(a) Determine the value of :
The value of is the number of data points provided. From the table, there are 5 rows (pairs of and ), so:
(b) Tabulate the results for , , , and :
We'll calculate (the square of ) and (the product of and ) for each data point:
0 | 0.10 | 0 | 0 |
3 | 0.13 | 9 | 0.39 |
5 | 0.14 | 25 | 0.70 |
8 | 0.17 | 64 | 1.36 |
10 | 0.19 | 100 | 1.90 |
(c) Calculate the values of and :
To calculate and , use the formulas:
Step 1: Compute the sums:
Step 2: Substitute into :
Step 3: Substitute into :
(d) Write the regression line:
The regression line is:
In terms of current () and voltage ():
Thus:
Would you like a detailed explanation of any specific part or further calculations?
Follow-up Questions:
- Why is calculating the regression line important in this experiment?
- How does relate to the physical properties of the circuit?
- What does the slope of the regression line represent in the context of the experiment?
- How would the regression line change if another data point was added?
- What is the significance of rounding values to 4 decimals in this calculation?
Tip: Always double-check your summations and calculations to ensure accuracy, especially when dealing with decimals.
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Summation
Slope and Intercept Calculation
Data Tabulation
Formulas
b = (nΣxy - ΣxΣy) / (nΣx² - (Σx)²)
a = (Σy - bΣx) / n
y = a + bx
Theorems
Least Squares Regression
Suitable Grade Level
Grade 11-12 or introductory college level
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