Correlation and RegressionMCQPYQ July 21Question 3709 of 188
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The straight - line graph of the linear equation y=a+bx\displaystyle y = a + bx, slope is horizontal if:

Options

Ab=1\displaystyle b = 1
Bb=0\displaystyle b = 0
Ca=0\displaystyle a = 0
Da=b=0\displaystyle a = b = 0
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Correct Answer

✅ Option b — b=0\displaystyle b = 0

All Options:

  • Ab=1\displaystyle b = 1
  • Bb=0\displaystyle b = 0
  • Ca=0\displaystyle a = 0
  • Da=b=0\displaystyle a = b = 0

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Detailed Solution & Explanation

For the linear equation y=a+bx\displaystyle y = a + bx, a\displaystyle a is the y\displaystyle y-intercept and b\displaystyle b represents the slope of the line. The slope of a line determines its angle of inclination with the horizontal x\displaystyle x-axis. - A horizontal line is parallel to the x\displaystyle x-axis, meaning its angle of inclination is 0∘\displaystyle 0^\circ. - The slope of a horizontal line is given by: Slope=tan⁡(0∘)=0\text{Slope} = \tan(0^\circ) = 0 Therefore, the line y=a+bx\displaystyle y = a + bx becomes horizontal when the slope b=0\displaystyle b = 0, reducing the equation to y=a\displaystyle y = a (a constant value for all x\displaystyle x). Hence, **Option B** is the correct answer.

About This Chapter: Correlation and Regression

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Correlation Coefficient, Regression Equations

This chapter covers Correlation Coefficient, Regression Equations and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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