Simple Linear Regression Analysis

2. Weight of Car: Miles gallon – Do heavier cars really use more gasoline? The following data were obtained from Consumer Reports (Vol 62 no. 4). Weight of car is in hundreds of pounds.

Car Weight 27 44 32 47 23 40 34 52
MPG 30 19 24 13 29 17 21 14

A simple linear regression of the model MPG = b0 + b1 WEIGHT
The results are shown below:

MPG & CAR WEIGHT
REGRESSION FUNCTION & ANOVA FOR MPG

MPG = 43.32625 - 0.600702 WEIGHT

R-Squared = 0.895426
Adjusted R-Squared = 0.877997
Standard error of estimate = 2.236055
Number of cases used = 8


Analysis of Variance

p-value
Source SS df MS F Value Sig Prob
Regression 256.87 1 256.87 51.37567 0.000372
Residual 29.99 6 4.99
Total 286.875 7

MPG & CAR WEIGHT
REGRESSION COEFFICIENTS FOR MPG

Two-Sided p-value
Variable Coefficient Std Error t Value Sig Prob
Constant 43.32625 3.23051 13.41156 0.000011
WEIGHT -0.60070 0.08381 -7.16768 0.000372 *

Standard error of estimate = 2.236055
Durbin-Watson statistic = 0.995097

Questions:

1. What sort of relationship exists between MPG and car weight?

2. Does the relationship make sense to you? Why or why not?

3. Test the hypotheses H0: b1 = 0 against H A: b1 ?0 a level of significance ? = 0.01. What is your conclusion?

MODEL: MPG= b0 + b1 WEIGHT

H0: b1 = 0

H A: b1 ? 0

4. What is your conclusion?

An automobile manufacturer has given its van a 47.1 47.1 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van performs under the manufacturer's MPG rating. After testing 140 140 vans, they found a mean MPG of 46.9 46.9 . Assume the population variance is known to be 4.41 4.41 . Is there sufficient evidence at the 0.02 0.02 level to support the testing firm's claim? Step 4 of 6 : Find the P-value of the test statistic. Round your answer to four decimal places.

Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by using different types of fuel. One vehicle of each size is tested. Does this sample provide sufficient evidence to conclude that there is a significant difference in treatment means?

  Click here for the Excel Data File

(a) Choose the correct statement.

• Fuel type is the blocking factor and vehicle size is the treatment.

• Fuel type is the treatment and vehicle size is the blocking factor.

(b) Fill in the boxes. (Round your SS values to 3 decimal places, F values to 2 decimal places, and other answers to 4 decimal places.)

(c) Choose the correct statement. Use α = 0.05.

• Fuel type means differ significantly and vehicle size is also a significant factor.

• Fuel type means do not differ significantly, but vehicle size is a significant factor.

• Fuel type means differ significantly, but vehicle size is not a significant factor.

• Fuel type means do not differ significantly and vehicle size is not a significant factor.

(d) Which fuel types show a significant difference in average fuel economy? Use α = 0.05. (You may select more than one answer. Click the box with a check mark for the correct answer and click to empty the box for the wrong answer.)

• Ethanol 10% and 87 Octane

• Ethanol 5% and 89 Octane

• 87 Octane and 91 Octane

• Ethanol 10% and 91 Octane

An automobile manufacturer has given its jeep a 31.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep performs under the manufacturer's MPG rating. After testing 110 jeeps, they found a mean MPG of 31.5. Assume the population standard deviation is known to be 1.8. Is there sufficient evidence at the 0.05 level to support the testing firm's claim?

Find the value of the test statistic. Round your answer to two decimal places.Specify if the test is one-tailed or two-tailed.

Find the P-value of the test statistic. Round your answer to four decimal places.

Identify the level of significance for the hypothesis test.

Make the decision to reject or fail to reject the null hypothesis.

An automobile manufacturer has given its jeep a 30.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 110 jeeps, they found a mean MPG of 30.5 . Assume the population variance is known to be 3.61 . Is there sufficient evidence at the 0.05 level to support the testing firm's claim?

Step 1: state the null & alternative hypothesis

Step 2 : Find the value of the test statistic. Round your answer to two decimal places.

Step 3: specify if it is a one or two tailed

step 4: find the p value of the test statistic

step 5: identify the level of significance of the hypothesis test

step 6: reject or fail to reject the hypothesis Please circle answers so I can follow steps properly

Fuel consumption is commonly measured in miles per gallon​ (mi/gal). An agency designed new fuel consumption tests to be used starting with 2008 car models. Listed below are randomly selected amounts by which the measured MPG ratings decreased because of the new 2008 standards. Find the​ range, variance, and standard deviation for the sample data. Is the decrease of 4​ mi/gal unusual? Why or why​ not?

22    

11    

33    

22    

44    

11    

33    

22    

22    

22    

22    

22    

11    

22    

22    

22    

11    

22    

22    

22

The range of the sample data is

nothing

​mi/gal. ​(Type an integer or a​ decimal.)The variance of the sample data is

nothing.

​(Round to one decimal place as​ needed.)The standard deviation of the sample data is

nothing

​mi/gal.

​(Round to one decimal place as​ needed.)

Is the largest​ decrease, 4​ mi/gal,

unusual​?

Why or why​ not?

A.

The decrease of 4​ mi/gal is unusual because the smallest value in a data set is usually an outlier.  

B.

The decrease of 4​ mi/gal is not unusual because the sample is a simple random​ sample, in which no values are considered unusual.

C.The decrease of 4​ mi/gal is

unusualunusual

because it is

more thanmore than

two standard deviations

fromfrom

the mean.

D.The decrease of 4​ mi/gal is

not unusualnot unusual

because it is

withinwithin

two standard deviations

ofof

the mean.

An automobile manufacturer has given its jeep a 48.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 250 jeeps, they found a mean MPG of 48.9. Assume the population variance is known to be 2.56. A level of significance of 0.01 will be used. Find the value of the test statistic. Round your answer to two decimal places.

Auto Expenses (LO. 2)

Cassandra owns her own business and drives her van 15,000 miles a year for business and 5,000 miles a year for commuting and personal use. She purchases a new van in 2018 and wants to claim the largest tax deduction possible for business use. Cassandra's total auto expenses for 2018 are as follows:

Determine Cassandra's 2018 deduction for business use of the van. (Note: The standard mileage rate for 2018 is 54.5 cents per mile.)

Round all amounts to the nearest dollar.

Cassandra can maximize her deduction by using the standard mileage deduction. Via this method, she can deduct $ for her van. Her other allocable expenses amount to $.____(answer here )_____

Travel Expenses (LO. 3)

Olga has to travel to Philadelphia for 2 days on business. She enjoys history and is planning to visit the Liberty Bell and other historic sites in the city. If time permits, she would like to make a side trip to nearby Gettysburg. A friend of Olga’s tells her, “The best part of traveling on business is that once the business is over, you can sightsee all you want and the cost is tax-deductible.” Olga, who is self-employed, has scheduled her trip for the Labor Day weekend so that she can spend 3 days sightseeing. Complete the letter to Olga which outlines the tax travel expense rules.

Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by using different types of fuel. One vehicle of each size is tested. Does this sample provide sufficient evidence to conclude that there is a significant difference in treatment means?

(a) Choose the correct statement.

• Fuel type is the blocking factor and vehicle size is the treatment.

• Fuel type is the treatment and vehicle size is the blocking factor.

(b) Fill in the boxes. (Round your SS values to 3 decimal places, F values to 2 decimal places, and other answers to 4 decimal places.)

(c) Choose the correct statement. Use α = 0.05.

• Fuel type means differ significantly and vehicle size is also a significant factor.

• Fuel type means do not differ significantly, but vehicle size is a significant factor.

• Fuel type means differ significantly, but vehicle size is not a significant factor.

• Fuel type means do not differ significantly and vehicle size is not a significant factor.

(d) Which fuel types show a significant difference in average fuel economy? Use α = 0.05. (You may select more than one answer. Click the box with a check mark for the correct answer and click to empty the box for the wrong answer.)

• Ethanol 10% and 87 Octane

• Ethanol 5% and 89 Octane

• 87 Octane and 91 Octane

• Ethanol 10% and 91 Octane

When speed limits were increased from 55 to 65 miles per hour a news item appeared in the Chicago Tribune, which showed that deaths on Illinois highways increased since the speed limits were raised to 65 mph. (a) Assuming that the faster speed caused the deaths, does this prove that cost-benefit analysis was not used in the decision to return to the 65 mph speed limit. (b) What is being implied if we do not go back to the 55 mph limit?