# 2477 Linear Regression Gradient & Y-intercept Formulae

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| By Anthony Nunan
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Anthony Nunan
Community Contributor
Quizzes Created: 136 | Total Attempts: 44,092
Questions: 24 | Attempts: 74

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. The three formulae used in this quiz are : General, y-intercept (a) and gradient (b)

• 1.

### We are trying to find the gradient of the least squares regression line.The Correlation Coefficient is 0.8.The mean of the x values is 12 and the mean of the y values is 30The standard deviation of the x values is 4 and the standard deviation of the y values is 8.What is the gradient?

Explanation
The App - rxsys2equ - the gradient only requires the correlation coefficient (r) and the SD for x and y.

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• 2.

### We are trying to find the gradient of the least squares regression line.The Correlation Coefficient is 0.7.The mean of the x values is 15 and the mean of the y values is 30The standard deviation of the x values is 6 and the standard deviation of the y values is 18.What is the gradient?

Explanation
The App - rxsys2equ - the gradient only requires the correlation coefficient (r) and the SD for x and y.

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• 3.

### We are trying to find the gradient of the least squares regression line.The Correlation Coefficient is 0.9.The mean of the x values is 18 and the mean of the y values is 34The standard deviation of the x values is 2 and the standard deviation of the y values is 6.What is the gradient?

Explanation
The App - rxsys2equ - the gradient only requires the correlation coefficient (r) and the SD for x and y.

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• 4.

### We are trying to find the gradient of the least squares regression line.The Correlation Coefficient is -0.9.The mean of the x values is 18 and the mean of the y values is 34The standard deviation of the x values is 4 and the standard deviation of the y values is 8.What is the gradient?

Explanation
The App - rxsys2equ - the gradient only requires the correlation coefficient (r) and the SD for x and y.

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• 5.

### We are trying to find the gradient of the least squares regression line.The Correlation Coefficient is 0.9.The mean of the x values is 6 and the mean of the y values is 29The standard deviation of the x values is 2 and the standard deviation of the y values is 8.What is the gradient?

Explanation
The App - rxsys2equ - the gradient only requires the correlation coefficient (r) and the SD for x and y.

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• 6.

### We are trying to find the gradient of the least squares regression line.The Correlation Coefficient is -0.9.The mean of the x values is 6 and the mean of the y values is 27The standard deviation of the x values is 4 and the standard deviation of the y values is 2.What is the gradient?

Explanation
The App - rxsys2equ - the gradient only requires the correlation coefficient (r) and the SD for x and y.

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• 7.

### We are trying to find the gradient of the least squares regression line.The Correlation Coefficient is -0.8.The mean of the x values is 6 and the mean of the y values is 27The standard deviation of the x values is 9 and the standard deviation of the y values is 4.5.What is the gradient?

Explanation
The App - rxsys2equ - the gradient only requires the correlation coefficient (r) and the SD for x and y.

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• 8.

### We are trying to find the y-intercept for the linear regression line.The gradient is given as 2.The mean of the x values is 4 and the mean of the y values is 8The standard deviation of the x values is 9 and the standard deviation of the y values is 4.5.What is the y intercept?

Explanation
The App - rxsys2equ - the y intercept only requires the gradient (b) and the mean of the x and y values.

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• 9.

### We are trying to find the gradient of the least squares regression line.The Correlation Coefficient is -0.6.The mean of the x values is 9 and the mean of the y values is 22The standard deviation of the x values is 7 and the standard deviation of the y values is 3.5.What is the gradient?

Explanation
The App - rxsys2equ - the gradient only requires the correlation coefficient (r) and the SD for x and y.

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• 10.

### We are trying to find the y-intercept for the linear regression line.The gradient is given as -2.The mean of the x values is -4 and the mean of the y values is 8The standard deviation of the x values is 7 and the standard deviation of the y values is 12.What is the y intercept?

Explanation
The App - rxsys2equ - the y intercept only requires the gradient (b) and the mean of the x and y values.

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• 11.

### We are trying to find the y-intercept for the linear regression line.The gradient is given as 0.5.The mean of the x values is 6 and the mean of the y values is 2The standard deviation of the x values is 9 and the standard deviation of the y values is 4.5.What is the y intercept?

Explanation
The App - rxsys2equ - the y intercept only requires the gradient (b) and the mean of the x and y values.

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• 12.

### We are trying to find the y-intercept for the linear regression line.The gradient is given as 2.The mean of the x values is 4 and the mean of the y values is 2The standard deviation of the x values is 9 and the standard deviation of the y values is 4.5.What is the y intercept?

Explanation
The App - rxsys2equ - the y intercept only requires the gradient (b) and the mean of the x and y values.

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• 13.

### We are trying to find the y-intercept for the linear regression line.The gradient is given as -0.5.The mean of the x values is 10 and the mean of the y values is 2The standard deviation of the x values is 9 and the standard deviation of the y values is 4.5.What is the y intercept?

Explanation
The App - rxsys2equ - the y intercept only requires the gradient (b) and the mean of the x and y values.

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• 14.

### We are trying to find the y-intercept for the linear regression line.The gradient is given as 0.5.The mean of the x values is 10 and the mean of the y values is 8The standard deviation of the x values is 9 and the standard deviation of the y values is 4.5.What is the y intercept?

Explanation
The App - rxsys2equ - the y intercept only requires the gradient (b) and the mean of the x and y values.

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• 15.

### We are trying to find the y-intercept for the linear regression line.The gradient is given as 1.The mean of the x values is 6 and the mean of the y values is 8The standard deviation of the x values is 5 and the standard deviation of the y values is 3.What is the y intercept?

Explanation
The App - rxsys2equ - the y intercept only requires the gradient (b) and the mean of the x and y values.

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• 16.

### We are trying to find the y-intercept for the linear regression line.The gradient is given as 0.5.The mean of the x values is 8 and the mean of the y values is 8The standard deviation of the x values is 9 and the standard deviation of the y values is 4.5.What is the y intercept?

Explanation
The App - rxsys2equ - the y intercept only requires the gradient (b) and the mean of the x and y values.

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• 17.

### We are trying to find the y-intercept for the linear regression line.The correlation coefficient is 0.9The mean of the x values is 4 and the mean of the y values is 8The standard deviation of the x values is 9 and the standard deviation of the y values is 4.5.What is the y intercept?

Explanation
The App - rxsys2equ - When you don't have the gradient (b) and you are looking for the y intercept, you should find both a & b.

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• 18.

### We are trying to find the y-intercept for the linear regression line.The correlation coefficient is 0.8The mean of the x values is 6 and the mean of the y values is 8The standard deviation of the x values is 18 and the standard deviation of the y values is 4.What is the y intercept to one decimal place?

Explanation
The App - rxsys2equ - When you don't have the gradient (b) and you are looking for the y intercept, you should find both a & b.

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• 19.

### We are trying to find the y-intercept for the linear regression line.The correlation coefficient is 0.8The mean of the x values is 5 and the mean of the y values is 8The standard deviation of the x values is 10 and the standard deviation of the y values is 15.What is the y intercept to one decimal place?

Explanation
The App - rxsys2equ - When you don't have the gradient (b) and you are looking for the y intercept, you should find both a & b.

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• 20.