Math Problem Statement
In the regression line π¦=β10+3π₯ :
The π¦ -intercept =0 and the slope =3 . The π¦ -intercept =β10 and the slope =3 . The π¦ -intercept =3 and the slope =β10 . The π¦ -intercept =β10 and the slope =β3 . The π¦ -intercept =10 and the slope =3 .
Solution
In the regression line equation , the general form is , where:
- represents the slope of the line,
- represents the y-intercept, which is the value of when .
From the given equation :
- The slope ,
- The y-intercept .
So, the correct statement is:
The y-intercept = -10 and the slope = 3.
Would you like any more details or explanations? Here are some related questions to think about:
- How does the slope of a line affect its direction?
- What is the significance of the y-intercept in a real-world context?
- How would the line change if the slope were negative?
- Can you rewrite the equation in terms of instead of ?
- How would you find the x-intercept of the line?
Tip: In regression, the slope represents the rate of change, and the y-intercept is the starting value when the independent variable is zero.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Regression
Slope-Intercept Form
Formulas
y = mx + b (Slope-Intercept Form)
Theorems
Slope-Intercept Theorem
Suitable Grade Level
Grades 8-10
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