Question

A study of emergency service facilities investigated the relationship between the number of facilities and the average distance traveled to provide the emergency service. The following table gives the data collected Number of Facilities 10 15 21 25 29 Average Distance (miles) 1.62 1.19 0.70 0.53 0.43 0.41 a. Choose the correct scatter diagram for these data, treating average distance traveled as the dependent variable A. Distance 1.5 0.5 15 20 25 30 Number 10

Answer 1

Regression ?X Input OK Input Y Range: SCS1:SCS7 Cancel Input X Range: SAS1:SBS7 Help □ Constant is Zero 95 Labels □ Confidence Level: % Output options SES3 O Qutput Range: O New Worksheet Ply: O New Workbook Residuals □ Residuals □ Standardized Residuals Normal Probability Residual Plots □ Line Fit Plots Normal Probability Plots 3. Click on OK.

The output is ression Statistics Multiple FR R Square Adjusted R Square Standard Error Observations 0.998873338 0.997747946 0.996246576 0.029955274 ANOVA MS Significance F Regression Residual Total 2 1.192641378 0.596321 664.5586 0.000106873 3 0.002691955 0.000897 5 1.195333333 coefficients standard Error t Stat P-value Lower 95% U 2.991094935 0.099135564 30.17176 8Е-05 2.675601326 3.306588544 0.159923565 0.010088923-15.8514 0.000546-0.192031021-0.127816109 r 95% Intercept Number of Facilities Number of Facilities Square 0.002470119 0.000232711 10.61452 0.001787 0.001729527 0.00321071 The regression model is Y = 2.99-0.160X+ 0.002X2 The coefficient of determination is 0.998 The procedure in Excel to run regression analysis for the second model is 1. Enter the data as shown below: 1 Number of Facilities 1/Number of Facilities Average Distance 1.62 1.19 0.7 0.53 0.43 0.41 10 15 21 25 29 0.10 0.07 0.05 0.04 0.03 0.03 4

2. Click on Data->Data Analysis->Regression->Click on OK->Enter the input and output as shown below Regression Input OK Input Y Range: SCS1:SCS7 SAS1:SBS7 Constant is Zero Cancel Input X Range: Help Labels | Confidence Level: 95 % Output options SES23 O Qutput Range O New Worksheet Ply O New Workbook Residuals Residuals Residual Plots □ Line Fit Plots □ Standardized Residuals Normal Probability Normal Probability Plots 3. Click on OK.

The output is ression Stotistics Multiple R R Square Adjusted R Square Standard Error Observations 0.992014521 0.98409281 0.973488016 0.079612384 ANOVA MS Significance F Regression Residual Total 2 1.176318938 0.588159 92.79698 0.002006274 3 0.019014395 0.006338 5 1.195333333 Coe ts standard Error tstat P-value Lower 95% Uer 95% Intercept Number of Facilities 1/Number of Facilities 0.2301530650.496965319 0.463117 0.674809 -1.351412377 1.811718508 0.0102550320.012679751 -0.80877 0.477836 -0.050607659 0.030097596 4.1673408 3.657272 0.035312 1.978762088 28.50343875 15.24110042 The regression model is y= 0.2 30-0.0 10X + 1 5.241 The coefficient of determination is 0.984

Note: If you don’t have Data Analysis plugin installed in your Excel then you install it by clicking on File->Options->Addins->Under Excel Add-ins Click on Go…->Check Analysis ToolPak and click OK. Now you will have Data Analysis option under Data Tab.