ZuoTi.Pro
Question

Simple Linear Regression Problem

QUESTION 7 A US consumer lobby wishes to develop a model to predict gasoline usage, as measured by miles per gallon, based on the weight of the car in pounds. The Excel data file AUTO.xls (contained in a folder under the CML Quizzes tab) contains data on this for fifty recent models. Use Excel Data Analysis to estimate a linear model for the relationship, a 95% confidence interval for as opecoefice and ha residua po State a numeric answers below correct to four decimal places using the Excel output results. 1. the intercept 2. the slope coefficient 3. the coefficient of determination 4. Using this model, predict the gasoline usage for a car weighing 3000 pounds. Use all decimal places in your calculation by selecting and using the values of bo and b1 in the output generated by Excel. 5. Does the prediction involve extrapolating the relationship? Type yes or no. State the 6. lower bound 7. upper bound and for the 95% confidence interval for the slope coefficient

math   Statistics-And-Probability   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

Paste the data in excel as shown below.

Weight Horsepower 1 MPG 2 48 110 105 165 139 103 115 155 142 150 71 76 65 100 84 58 43.1 1985 19.9 3365 19.23535 17.73445 18.1 3205 20.3 2830 21.5 3245 16.9 4360 15.5 4054 18.5 3940 27.2 3190 41.5 2144 46.6 2110 23.7 2420 27.2 2490 39.1 1755 28 2605 24 2865 10 12 13 15 16 17 18 19 20 20.2 3570 20.5 3155 28 2678 34.7 2215 92 139 95 90 63 23
In the data tab, click on data analysis and select the regression option.

Data Analysis Analysis Tools OK Histogram Moving Average Random Number Generation Rank and Percentile Regression Sampling t-Test: Paired Two Sample for Means t-Test: Two-Sample Assuming Equal Variances t-Test: Two-Sample Assuming Unequal Variances z-Test: Two Sample for Means Cancel Help

Input the data range in the regression dialog box as shown below.

Regression Input OK $A$1:$A$51 $B$1:$B$51 Constant is Zero Input Y Range: Cancel Input X Range: Help Labels Confidence Level: 95 Output options 0) Output Ran $G$1 O New Worksheet Ply New Workbook Residual:s □ Residuals □ Residual Plots Line Fit Plots Standardized Residuals Normal Probability Normal Probability Plots

The following output will be generated as shown below,

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.82480863 0.680309276 0.673649053 4.668104259 50 ANOVA df MS gnificance F Regression Residual Total 1 2225.864 2225.864 102.1451 1.79E-13 48 104977 21.7912 49 3271.842 Intercept Weight Coefficients andard Err t Stat P-value Lower 95%Upper 95969wer 95.0%pper 95.0% 57.7972526 2.96897 19.4671 2.01E-24 51.82774 63.76677 51.82774 63.76677 0.010613111 0.00105 -10.1067 1.79E-130.01272 0.0085 -0.01272 -0.0085
1. the intercept (highlighted in green):57.7972526

2. the slope coefficient (highlighted in blue): -0.010613111

3. the coefficient of determination (highlighted in yellow): 0.680309276

4. Using the model, predict the gasoline usage for a car weighing 3000 pounds

y = 57.7972526 - -0.010613111 (pound)
y =57.7972526 - -0.010613111 (3000)= 25.95791975

5. Does the prediction extrapolate the relation? No

6. lower bound -0.012724494

7 upper bound -0.008501728 for the 95% confidence interval for the slope coefficient

0 0
Add a comment
Know the answer?
Add Answer to:
Simple Linear Regression Problem QUESTION 7 A US consumer lobby wishes to develop a model to...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • Simple Linear regression 1. A researcher uses a simple linear regression to measure the relationship between...

    Simple Linear regression 1. A researcher uses a simple linear regression to measure the relationship between the monthly salary (Salary measured in dollars) of data scientists and the number of years since being awarded a Master degree (Master Degree). A random sample of 80 observations was collected for the analysis. A researcher used the econometric model which has the following specification Salary,-β0 + β, Master-Degree, + εί, where i = 1, , 80 The (incomplete) Excel output of equation (1)...

  • 1. Using question 12 (delaying major purchases) as the response variable (Y) compute a regression model...

    1. Using question 12 (delaying major purchases) as the response variable (Y) compute a regression model with the following questions 9, 25 (gender: males as 0 and females coded as 1) as your predictor variables. You will have to use the data set Economic Gun Legislation Survey Regression Exercise posted for Week 9 on the webpage. Please do the following in exactly this order: a. Excel Output b. Model: write down model like in form y- b, b,X, -b.X. +...

  • please help! Following is a simple linear regression model: y = a + A + &...

    please help! Following is a simple linear regression model: y = a + A + & The following results were obtained from some statistical software. R2 = 0.523 Syx (regression standard error) = 3.028 n (total observations) = 41 Significance level = 0.05 = 5% Variable Interecpt Slope of X Parameter Estimate 0.519 -0.707 Std. Err. of Parameter Est 0.132 0.239 Note: For all the calculated numbers, keep three decimals. Write the fitted model (5 points) 2. Make a prediction...

  • Part 2: Simple Linear Regressions – Chapter 14 (2 questions with a total of 11 sub-sections,...

    Part 2: Simple Linear Regressions – Chapter 14 (2 questions with a total of 11 sub-sections, 6 points per sub-section, part total 66 points) 2) A local grocery store wants to predict its daily sales in dollars (y). The manager believes that the amount of newspaper advertising (x) significantly affects sales. He randomly selects 7 days of data (n=7) consisting of daily grocery store sales (y, in thousands of dollars) and advertising expenditures (x, in thousands of dollars). The Excel...

  • Using your simple linear regression​ model, what is the value for the slope for this regression​...

    Using your simple linear regression​ model, what is the value for the slope for this regression​ model? Take a Test-Mohammad (2) Exploring bivariatenu x+ Nick James . YouTube × Co https://www.mathxl.com/Student/PlayerTest.aspx?tesA 11 □ Bunnings Canvas晏Fisher Library Study dates Other bookmarks 21 BUSS1020 Quantitative Business Analysis Nurullah | 5/30/19 4:13 AM Test: Assignment 2 This Question: 1 pt 6 af 20 This Test: 20 pts possible A national restaurant chain is composed of 6500 restaurants, sach of which is located in...

  • Simple Linear Regression Problem 3 points Save Answer QUESTION 1 The standard error of the estimate...

    Simple Linear Regression Problem 3 points Save Answer QUESTION 1 The standard error of the estimate is the amount of error that is calculated amongst variables the same amount of error throughout, hence being standard the measure of variability around the line of regression the measure of the volatility of the independent variable 2 pointsSave Answer QUESTION 2 The Maroochy Chamber of Commerce is interested in determining the relationship between the number of fine days each year and the number...

  • Problem 5- Simple Linear Regression The following data represent the number of flash drives sold per...

    Problem 5- Simple Linear Regression The following data represent the number of flash drives sold per day at a local computer shop and their prices Price $34 36 32 35 30 Units Sold 6 40 A computer output is produced to examine this relationship further SUMMA RY OUTPUT Regression Statistics Multiple R RSquare Adjusted R Square Standard Error Observations 0.924982 0.855592 0.826711 1.119949 7 ANOVA MS gnificance F Regression Residual Total 137.15714 37.15714 29.62415 0.002842 5 б,271429 1.254286 6 43.42857...

  • A researcher developed a regression model to predict the tear rating of a bag of coffee...

    A researcher developed a regression model to predict the tear rating of a bag of coffee based on the plate gap in​ bag-sealing equipment. Data were collected on 2828 bags in which the plate gap was varied. An analysis of variance from the regression showed that b1equals=0.79240.7924 and Upper S Subscript b 1Sb1equals=0.20940.2094. a. At the 0.05 level of​ significance, is there evidence of a linear relationship between the plate gap of the​ bag-sealing machine and the tear rating of...

  • A home appraisal company would like to develop a regression model that would predict the selling...

    A home appraisal company would like to develop a regression model that would predict the selling price of a house based on the age of the house in years (Age), the living area of the house in square feet (Living Area) and the number of bedrooms (Bedrooms). The given Excel output shows the partially completed regression output from a random sample of homes that have recently sold. How many homes were included in the sample? EEB Click the icon to...

  • Consider the simple linear regression model: HARD1 = β0 + β1*SCORE + є, where є ~...

    Consider the simple linear regression model: HARD1 = β0 + β1*SCORE + є, where є ~ N(0, σ). Note: HARD1 is the Rockwell hardness of 1% copper alloys and SCORE is the abrasion loss score. Assume all regression model assumptions hold. The following incomplete output was obtained from Excel. Consider also that the mean of x is 81.467 and SXX is 81.733. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square 0.450969 Standard Error Observations 15 ANOVA df...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT