2. The raw material used in the production of a certain synthetic fiber is stored in a location without a humidity control. Measurements of relative humidity in the storage location and the moisture content of a sample of the raw material were taken over 15 days with the following data (in percentages) resulting. relative humidity 46 53 29 61 36 39 47 49 52 38 55 32 57 54 44 Moisture content 12 15 7 17 10 11 11 12 14 9 16 8 18 14 12 Estimate regression line for above given data. ANS: regression line is Y = −2.51 + 0.32x

To estimate the regression line, we use the linear regression formula:

\[
Y = a + bX
\]

where:
- \( Y \) is the dependent variable (moisture content),
- \( X \) is the independent variable (relative humidity),
- \( a \) is the y-intercept,
- \( b \) is the slope of the line.

Using statistical methods to calculate the slope \( b \) and intercept \( a \), we find:

\[
Y = -2.51 + 0.32X
\]

This line implies that:
- For each 1% increase in relative humidity, the moisture content in the material increases by 0.32%.
- When the relative humidity is 0%, the estimated moisture content would theoretically be -2.51%. (In practice, this point is theoretical and serves as the line’s intercept in this context.)

Would you like a step-by-step breakdown of the calculations involved in determining this regression line?

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Here are five related questions to deepen your understanding:

1. How would the regression line change if the moisture content values were significantly higher?
2. What is the significance of the slope value in the context of this data?
3. How would outliers in the data affect the estimated regression line?
4. Can this regression line be used to predict moisture content accurately beyond the measured humidity range?
5. How can we assess the strength of the relationship between relative humidity and moisture content?

**Tip:** In regression analysis, always check for outliers, as they can significantly influence the slope and intercept, potentially leading to a misleading regression line.

The raw material used in the production of a certain synthetic fiber is stored in a location without a humidity control. Measurements of relative humidity in the storage location and the moisture content of a sample of the raw material were taken over 15 days with the following data (in percentages) resulting. relative humidity 46 53 29 61 36 39 47 49 52 38 55 32 57 54 44 Moisture content 12 15 7 17 10 11 11 12 14 9 16 8 18 14 12 Estimate regression line for above given data. ANS: regression line is Y = −2.51 + 0.32x

Learn how to estimate the regression line for moisture content based on relative humidity data. The regression line is calculated as Y = -2.51 + 0.32X, where X represents relative humidity and Y is the moisture content. Suitable for students in Grades 9-12 studying linear regression.

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