Question

1. What does the error term in the simple linear regression model account for?
   
   
   
   
2. What are the parameters of the simple linear model
   
   
   
   
3. When all the points fall on the regression line, what is the value of the correlation coefficient?
   
   
   
4. Part of an Excel output relating 15 observations of X (independent variable) and Y (dependent variable) is shown below. Provide the values for a-e shown in the table below. (See section 15.5)

Summary Output

ANOVA
	df	SS	MS	F	Significance F
Regression	1	2.7500	-d-	-e-	0.632
Residual	-a-	-b-	11.45
Total	14	-c-

5. A Company has recorded data on daily demand for its product (y in thousands of units) and the unit price (x in hundreds of dollars). A sample of 10 days demand and associated prices resulted in the following summary data. Use the information to answer the questions below.

                                      

                                     

                                                   

1. Compute b₁
   
   
   
2. Compute b₀
   
   
3. Use the least squares method to develop and write the estimated regression the equation.

4. What type of relationship exists between x and y? Explain.

5. Would the demand ever reach zero? If yes, at what price would the demand be zero?

6. Compute the coefficient of determination and the correlation coefficient?

Answer 1

"As per the HOMEWORKLIB RULES, we need to answer for the first question only in multiple posting. Please ask single question in single post."

1) What does the error term in the simple linea regression model account for?
The error term refers to the sum of deviations within the regression line.It explains the difference between the theoretical value of the model and the actual observed result.

Suppose we have a multiple linear regression function of the form Y=+X_i+_i

where and are constant parameters

X_i is  independent variables and

_i is error term

2)What are the parameters of the simple linear model?

The parameter is the intercept and represents the expected response when X_i=0.

The parameter is the slope and represents the expected increment in the response per unit change in X_i.

3) When all the points fall on the regression line, what is the value of the correlation coefficient?

When all the points fall on the regression line,the value of the correlation coefficient would be equal to 1.

There are two situation with value of r.

When r=-1,the graph is as follows.It shows a negative trend.

When r=+1,the graph is as follows.It shows a positive trend.