MTH 305 Midterm Exam Complete Solution
Assignment 3
Possible Total Points: 60 pts
Instructions:
 Turn in your answers in paperform (handwritten or typed) by the beginning of class.
 Include complete sentences and show all calculations.
 Each question is equally weighted.
 Partial credit is possible even if an answer is incomplete.
EXERCISE #1. Ch. 13 (section 13.2): Problem #13.1 (p. 523)
 Fitting a straight line to set a data yields the ff prediction line
Yi=2+5Xi
 Interpret the meaning of the Y intercept b0.
 Interpret the meaning of the slope b1
 Predict the mean value of Y for X=3
EXERCISE #2. Ch. 13 (section 13.2): Problem #13.9 all except part (a) (p. 525)
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?
For part (b): 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 
EXERCISE #3. Ch. 13 (section 13.3): Problem #13.21 (p. 531)
In problem 13.9 on page 255 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.
 Determine the coefficient of the determination r^2 and interpret its meaning.
 Determine the standard error of the estimate.
 How useful do you thing this regression model is for predicting the monthly year?
For parts (a) and (b): To get the intercept r2 and the standard error you can use the output from the “Regression Analysis” function you got for Problem #13.19 above (see Exercise #2), or type these commands in any Excel cell:
=RSQ(range of Y data, range of X data)
=STEYX(range of Y data, range of X data)
EXERCISE #4. Ch. 14 (section 14.6): Problem #14.38 (p. 600)
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
 Interpret the meaning of the slope for variable X1.
 Interpret the meaning of the slope for variable X2
 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?
EXERCISES #5 & 6. Ch 14: Problem #14.72 all part except (d) and (i) (p. 613)
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.
 State the multiple regression equation.
 Interpret the meaning of the slopes in this equation.
 Predict the gasoline mileage for an automobile for an automobile that has the length of 195 inches and weight of 3,000 pounds.
e )Is there a significant relationship between gasoline mileage and the two independent variables (length and weight) at the 0.5 level of significance.
f)Determine the pvalue in (e) and interpret its meaning.
g) Interpret the meaning of the coefficient of multiple determination in this problem.
h ) Determine the adjusted r2.
j) Determine the pvalue 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).
k) Construct a 95% confidence interval estimate of the population slope between gfasoline mileage and weight.
l) 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  6.20871E24  
Residual  117  1019.867258  8.716814173  
Total  120  2627.289256 


 
 Coefficients  Standard Error  t Stat  Pvalue  Lower 95%  Upper 95% 
Intercept  42.43290086  8.218578926  5.163045977  1.00728E06  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  5.3858E13  0.00606673  0.00368720 
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