Question

In: Statistics and Probability

How are the slope and intercept of a simple linear regression line calculated? What do they...

How are the slope and intercept of a simple linear regression line calculated? What do they tell us about the relationship between the two variables? Give example of problem.

Solutions

Expert Solution

the following data are passed:

Time of study Mark
3 32
8 56
8 78
9 63
5 12

The independent variable is Time of studyTimeofstudy, and the dependent variable is MarkMark. In order to compute the regression coefficients, the following table needs to be used:

Time of study Mark Time of study*Mark Time of study2 Mark2
3 32 96 9 1024
8 56 448 64 3136
8 78 624 64 6084
9 63 567 81 3969
5 12 60 25 144
Sum = 33 241 1795 243 14357

Based on the above table, the following is calculated:


Related Solutions

How are the slope and intercept of a simple linear regression line calculated? What do they...
How are the slope and intercept of a simple linear regression line calculated? What do they tell us about the relationship between the two variables? Also, give an example.
simple linear regression proof of variance of intercept estiamtor β0
simple linear regression proof of variance of intercept estiamtor β0
Simple Linear Regression Explain with Your Example : no need for any line drawing 1)Slope b1=...
Simple Linear Regression Explain with Your Example : no need for any line drawing 1)Slope b1= Beta positive or Negative is positive ? 2)b0 is the y intercept of the line.? 3)Equation; Linear regression equation= 4)y is the estimated value of y for a given x value. 5)Coefficient of Determination Explain If r = 0.8584t   then R to power 2 (r^2 =?) Would be ? What is it mean and interpretation of it.
In a simple linear regression analysis, will the estimate of the regression line be the same...
In a simple linear regression analysis, will the estimate of the regression line be the same if you exchange X and Y? Why or why not?
show graphically and explain how the x-intercept, the y-intercept and the slope of the budget line...
show graphically and explain how the x-intercept, the y-intercept and the slope of the budget line changes for each of the following scenarios a. The price of X changes b. the price of y changes c. Money income changes
In simple linear regression, describe (in words) how the parameters of the equation of the line...
In simple linear regression, describe (in words) how the parameters of the equation of the line (i.e., bo and b1) are determined?
Create a class defined for Regression. Class attributes are data points for x, y, the slope and the intercept for the regression line.
Python:Create a class defined for Regression. Class attributes are data points for x, y, the slope and the intercept for the regression line. Define an instance method to find the regression line parameters (slope and intercept). Plot all data points on the graph. Plot the regression line on the same plot.
6. In the simple linear regression model, the y-intercept represents the: a. change in y per...
6. In the simple linear regression model, the y-intercept represents the:a. change in y per unit change in x.b. change in x per unit change in y.c. value of y when x=0.d. value of x when y=07. In the simple linear regression model, the slope represents the:a. value of y when x=0.b. average change in y per unit change in x.c. value of x when y=0.d. average change in x per unit change in y.8. In regression analysis, the residuals...
Why does the intercept estimator in simple linear regression follow a normal distribution. Justify this by...
Why does the intercept estimator in simple linear regression follow a normal distribution. Justify this by using the appropriate assumptions of simple linear regression.
You wish to estimate as precisely as possible the slope β1 in the simple linear regression...
You wish to estimate as precisely as possible the slope β1 in the simple linear regression model yi = β0 + β1xi + ei , i = 1, . . . , 4. Each pair of observations (xi , yi) costs $ 1:00 and your budget is $ 4:00. A data analyst proposes that you consider one of the following two options: (a) Make two y-observations at x = 1 and a further two at x = 4; (b) Make...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT