Reference no: EM13928325

Question 1:

Fitting a straight line to set a data yields the ff prediction line Yi=2+5Xi

 

1. Interpret the meaning of the Y intercept b0.
2. Interpret the meaning of the slope b1
3. Predict the mean value of Y for X=3

Question 2:

An  agent for residential real estate company in a large  city would like  to be able to predict the monthly rental cost for apartments based on the  size of the apartment as defined by square footage. A sample of 25 apartment RENT in a particular residential neighborhood was selected, and the information gathered revealed the following

Apartment    Monthly Rent ($)    Size ( Square Feet)    Apartment       Monthly Rent          Size

1                       950                           850                      14                1,800                  1,369

2                     1,600                         1,450                     15               1,400                  1,175

3                     1,200                         1,085                     16                1,450                 1,225

4                     1,500                         1,232                     17                1,100                 1,245

5                      950                            718                       18                1,700                 1,259

6                     1,700                         1,485                      19               1,200                  1,150

7                     1,650                         1,136                       20               1,150                  896

8                      935                            726                         21               1,600                1,361

9                      875                            700                         22               1,650                1,040

10                   1,150                           956                         23               1,200                  755

11                   1,400                         1,100                         24                800                 1,000

12                   1,650                         1,285                         25               1,750               1,200

13                   2300                          1,985    

14                   1,800                          1,369

15                   1,400                          1,175

b)  Use the least -squares method to find the regression coefficients b0 and b1.

c) Interpret the meaning of b0 and b1 in this problem.

d) Predict the mean monthly rent for an apt. that has 1,000 square feet.

e)  Why would it not be appropriate to use the model to predict the monthly rent for apts. That have 500 square feet?

f) Your friend Jim and Jennifer are considering signing a lease for an apt. in this residential neighborhood. They are trying to decide between two apts, one with 1,000 square feet for a monthly rent of 1,275 and the other with 1,200 square feet for a monthly rent of 1,425. What would you recommend to them? Why?

Question 3:

Below is the dataset you need to solve this problem in Excel. To get the intercept b0 and slope b1, you can use the "Regression Analysis" function in Excel or type these commands in any Excel cell:

=SLOPE(range of Y data, range of X data)

=INTERCEPT(range of Y data, range of X data)

Rent	Size
950	850
1600	1450
1200	1085
1500	1232
950	718
1700	1485
1650	1136
935	726
875	700
1150	956
1400	1100
1650	1285
2300	1985
1800	1369
1400	1175
1450	1225
1100	1245
1700	1259
1200	1150
1150	896
1600	1361
1650	1040
1200	755
800	1000
1750	1200

Question 4:

An agent for real estate company wanted to predict the monthly rent for apts. Based on the size of the apt. Rent using of the apt, RENT using the results of that problem.

1. Determine the coefficient of the determination r^2 and interpret its meaning.
2. Determine the standard error of the estimate.
3. How useful do you thing this regression model is  for predicting the monthly year?

Question 5:

 

Suppose X1 is a numerical variable and X2 is a dummy variable and the following regression equation for a sample n= 20 is:   Y1 = 6+4 x 1i + 2X 2i

1. Interpret the meaning of the slope for variable X1.
2. Interpret the meaning of the slope for variable X2
3. Suppose that the t statistic for testing the contribution of variable X2 is 3.27. At the 0.05 level of significance, is there evidence that variable X2 makes a significant contribution to the model?

Question 6:

 

The file AUTO2002 contains data on 121 automobile models from the year 2002. Among the variables included are the gasoline mileage ( in miles per gallon), the length ( in inches), and the weight (in pounds) of each automobile. Develop a model to predict the gasoline mileage based on the length and weight of each automobile.

1. State the multiple regression equation.
2. Interpret the meaning of the slopes in this equation.
3. Predict the gasoline mileage for an automobile for an automobile that has the length of 195 inches and weight of 3,000 pounds.

A) Is there a significant  relationship between gasoline mileage and the two independent variables (length and weight) at the 0.5 level of significance.

B) Determine the p-value in (e) and interpret its meaning.

C) Interpret the meaning of the coefficient of multiple determination in this problem.

D) Determine the adjusted r2.

E) Determine the p-value in (i) and interpret their meaning. ( (i)= At the 0.05 level of significance, determine whether each independent variable makes a significant contribution  to the regression model. Indicate the most appropriate regression model for this set of data).

F) Construct a 95% confidence interval estimate of the population slope between gfasoline mileage and weight.

G) Compute and interpret the coefficients of partial determination.

The Excel output for this exercise is given below. Use this output to answer the questions.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.782187748
R Square	0.611817673
Adjusted R Square	0.60186428
Standard Error	2.952425134
Observations	121
ANOVA
	df	SS	MS	F	Significance F
Regression	3	1607.421998	535.8073326	61.46825227	6.20871E-24
Residual	117	1019.867258	8.716814173
Total	120	2627.289256
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	42.43290086	8.218578926	5.163045977	1.00728E-06	26.15643651	58.70936521
Length	-0.00667189	0.036217633	-0.18421688	0.854162226	-0.07839902	0.065055222
Width	-0.03989444	0.182924039	-0.21809293	0.827736634	-0.40216590	0.322377022
Weight	-0.00487697	0.000600754	-8.11807648	5.3858E-13	-0.00606673	-0.00368720