1In constructing the regression model the x values lie betwe

1.In constructing the regression model the x values lie between $4.95 and $6.95 for a predicted equation Y= 6 - 3X. Can we estimate Y when x=$7.95? Comment.

2.What are the regression coefficients in the simple linear regression model?

3.The regression line always passes through the mean of x and y. True or False.

4. What are the assumptions of linear regression model?

5. What are outliers?  

Solution

1. Extrapolation is making a prediction outside the range of values of the predictor in the sample used to generate the model. The more removed the prediction is from the range of values used to fit the model, the riskier the prediction becomes because there is no way to check that the relationship continues to be linear.

Y = 6 -3*7.95 = $-17.85

This gives a absurd value so, we cannot extrpolate

2. In Y = 6 - 3X

Regression coefficients : b = -3 ( slope ) measures the steepness of the regression line

a = 6 is the y intercpt constant

3. If we take the mean of Y and subtract the slope times the mean of X. Now it turns out that the regression line always passes through the mean of X and Y

So, True

4. Linear regression needs the relationship between the independent and dependent variables to be linear.It checks four assumptions:

a) Linear relationship

b) The linear regression analysis requires all variables to be multivariate normal.

c) linear regression assumes that there is little or no multicollinearity in the data

d) linear regression analysis requires that there is little or no autocorrelation in the data. Autocorrelation occurs when the residuals are not independent from each other.  

5) Data points are clustered towards the one corner of the scatter plot, there are a few points which lie far away from the main cluster of the data. These points are known as outliers, and depending on their location may have a major impact on the regression line.