Question

Camp Rainbow offers overnight summer camp programs for children ages 10-14 every summer during June and July. Each camp session is one week and can accommodate up to 200 children. The camp is not coed, so boys attend during the odd-numbered weeks and girls attend during the even- numbered weeks. While at the camp, participants make crafts, participate in various sports, help care for the camp's resident animals, have cookouts and hayrides, and help assemble toys for local underprivileged children. The camp provides all food as well as materials for all craft classes and the toys to be assembled. One cabin can accommodate up to 10 children, and one camp counselor is assigned to each cabin. Three camp managers are on- site regardless of the number of campers enrolled. Following is the cost information for Camp Rainbow's operations last summer: WeekNumber of CampersCost to Run Camp 162 $11,070 158 11,600 144 10,600 180 13,730 9,000 13,750 8,090 122 10,000 June aaaa Required: 1. Perform a least-squares regression analysis on Camp Rainbow's data. Intercept: X variable 1: 2. Using the regression output, create a cost equation (y = a + bx) for estimating Camp Rainbow's operating costs. 3. Using the least squares regression results, calculate the camp's expected operating cost if 96 children attend a session.

Answer 1

Step-1:

Week Regression Statistics (ANOVA) Coefficients Intercept 3442.88 Revenues 52.62 # of Campers Run Cost 162 $11,070 158 $11,600 144 $10,600 180 $13,730 92 $9,000 $13,750 $8,090 22 $10,000 2) Cost equation (y=a+bx) = $3442.88 + ($52.62x) 192 96 3) Expected operating costs equals to $3442.88 + ($52.62 x 96) = $3442.88 + $5051.52 = $8,494.40 Step-1: Insert data in an Excel sheet in cell numbers: A1 thru 09. Press 'Data' tab and then 'Data Analysis' option at the right-hand side on top of the page. Step-3: Insert cell reference $C$2:$C$9 against 'Input Y Range' cell as # of Run. Cost is the dependent variable. Insert cell reference $B$2:$B$9 against 'Input X Range' cell as # of Campers is independent variable. After that, press 'OK' tab on the pop-up window itself. Step-2: Press 'Regression' option and then 'OK' tab on the pop-up window. Step-4 (Final): SUMMARY OUTPUT and ANOVA table will be generated by Excel in a separate sheet. From there, required results are traced.

Data Analysis File Home Insert Page Layout Formulas Data Review E 2 Show Queries > Connections ALZA From Table 3 Properties Get External New Refresh Z Sort Data Query - Lo Recent Sources All ] Edit Links Get & Transform Connections View Tell me what you want to do... Y Clear E Flash Fill s Reapply -1 Remove Duplicates Filter Text to " Advanced Columns Data Validation - Sort & Filter Data Tools - Consolidate Relationships Manage Data Model Group - Ungroup -- Subtotal What-If Forecast Analysis Sheet Forecast Outline A Week D E F G H I J K L M N O Analysis Data Analysis Tools Tools for financial and scientific data analysis. FUNCRES Tell me more 1 1 nm todo B # of Campers 162 158 144 180 92 Nm 7 in C Run Cost $11,070 $11,600 $10,600 $13,730 $9,000 $13,750 $8,090 $10,000 192 96 8 122

Step-2:

Review ELE Data Analysis + File Home Insert Page Layout Formulas Data Show Queries Connections Get External New From Table E Properties Refresh Edit links Lo Recent Sources Query Get & Transform Connections View Tell me what you want to do... Clear 2 Flash Fill 1-- Consolidate Reapply 5 Remove Duplicates e Relationships Text to y Advanced Columns Data Validation - Manage Data Model Sort & Filter Data Tools Group. Ungroup -- Subtotal Āj Sort Filter What If Forecast Analysis Sheet Forecast Outline Analysis A Week D E F G H I J K L | м. N O P Q R 1 1 2 amino mt no 00 B # of Campers 162 158 144 180 92 192 96 122 C Run Cost $11,070 $11,600 $10,600 $13,730 $9,000 $13,750 $8,090 $10,000 Data Analysis Х OK Tancel Analysis Tools Histogram Moving Average Random Number Generation Renkand Dercentile Regression Sampung 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 Help 15 16 17

Step-3:

Review Data Analysis Home Insert Page Layout Formulas Data Show Queries Connections From Table Get External New 9 Properties Refresh Data Query - Lo Recent Sources All Edit Links Get & Transform Connections View Tell me what you want to do... Clear E Flash Fill b-Consolidate Reapply 5 Remove Duplicates e Relationships Filter Text to Advanced Columns Data Validation - Manage Data Model Sort & Filter Data Tools Group + Ungroup -- Subtotal Z Sort What If Forecast Analysis Sheet Forecast Outline Analysis G H I J K L M N O P Q R 1 Week 1 Regression 2 amino # of Campers 162 158 144 180 92 Input Гок | Run Cost $11,070 $11,600 $10,600 $13,730 $9,000 $13,750 $8,090 $10,000 Jnput Y Range: $C$2:$C$9 Cancel Input X Range: $B$2:$B$9 192 96 Help 122 Labels Confidence Level: Constant is Zero 95 % 15 Output options O Qutput Range: O New Worksheet Ply: O New Workbook Residuals Residuals Standardized Residuals 16 17 Residual Plots Line Fit Plots Normal Probability Normal Probability Plots

Step-4:

Connections 4L A4 O Data Analysis File Home Insert Page Layout Formulas Data Review E 2 Show Queries Connections A, ZA From Table 9 Properties Get External New Refresh Z Sort Data Query - Lo Recent Sources Get & Transform Connections View Tell me what you want to do... Clear 2 Flash Fill - Consolidate 5 Remove Duplicates e Relationships Filter Text to V Advanced Data Validation - Columns – Manage Data Model Sort & Filter Data Tools Reapply Group * Ungroup -- Subtotal What If Forecast Analysis · Sheet Forecast Outline Analysis L11 в с D E F G H I J K L M N 1 SUMMARY OUTPUT 2 8 Regression Statistics 4 Multiple R 0.957586536 5 R Square 0.916971974 6 Adjusted R Square 0.90313397 7 Standard Error 633.5409085 8 Observations 9 10 ANOVA 11 df 12 Regression 1 13 Residual 6 14 Total 7 Significance F 0.000184728 SSM S 26596955.5 26596955.5 66.26475562 2408244.496 401374.0827 29005200 15 17 Intercept 18 X Variable 1 19 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 3442.880562 $52.6083255 3.614161739 0.011175056 1111.931961 5773.829163 1111.931961 5773.829163 52.61514442 6.463525499 8.140316678 0.000184728 36.79946727 68.43082156 36.79946727 68.43082156