Question

need assistance with this question from my homework but I only needs part B and D

Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets having diameters smaller than 10 um (mg/m3): х 86 177 190 354 364 442 970 y 0.42 0.60 0.51 0.66 0.60 0.69 0.95 (a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy? Yes, a scatter plot shows a reasonable linear relationship. O No, a scatter plot does not show a reasonable linear relationship. (b) What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? (Round your answer to three decimal places.) .964

Answer 1

Use the Excel's 'Data Analysis' add-in from the 'Data' tab as shown below to access the 'Regression' option -

File Home Insert Draw Page Layout Formulas Data Review View Help Power Pivot Share Queries & Connections Data Analysis Recent Sources [9 Existing Connections M From Text/CSV Le From Web Get Data From Table/Range AL JA Z B Group Ungroup انار انا Clear Reapply Advanced E B Properties Refresh All Edit Links ? Solver Stocks Geography Sort Filter Text to Columns Es What-If Forecast Analysis Sheet Subtotal Get & Transform Data Queries & Connections Data Types Sort & Filter Data Tools Forecast Outline Analyze B1 X Y A B с D E F G H J K L M N O Р o R S T U V 1 x 2 86 0.42 Data Analysis ? X 0.6 3 4 177 190 0.51 OK 354 Cancel 5 6 0.66 0.6 364 7 442 970 Help Analysis Tools Covariance Descriptive Statistics Exponential Smoothing F-Test Two-Sample for Variances Fourier Analysis Histogram Moving Average Random Number Generation Rank and Percentile Regression 0.69 0.95 8 9 10 11 12

Then input the 'X' and 'Y' data and make sure to mark the option 'labels' and then click 'Ok' as shown -

Get & Transform Data Regression ? х B1 X fr Y Input Input Y Range: OK А B 1 C D $B$1:$B$8 Cancel Y Input X Range: $A$1:$A$8 1 86 1 X 2 3 4 Help Labels Confidence Level: Constant is Zero 95 % 177 190 354 364 442 970 0.42 0.6 0.51 0.66 0.6 0.69 0.95 6 1 8 Output options O Qutput Range: New Worksheet Ply: New Workbook Residuals Residuals Standardized Residuals 10 11 Residual Plots Line Fit Plots Normal Probability Normal Probability Plots 12 13 14 15 16 17 18 19

This would give following output -

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.964095845
R Square	0.929480798
Adjusted R Square	0.915376958
Standard Error	0.048552612
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.155356076	0.155356076	65.90267455	0.000460162
Residual	5	0.011786781	0.002357356
Total	6	0.167142857
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0.430340479	0.03096921	13.89575269	3.46811E-05	0.350731591	0.509949366
X	0.000548826	6.76056E-05	8.118046227	0.000460162	0.00037504	0.000722611

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(b) Note that the coefficient of determination (R-square) tells us about the amount of variation in dependent variable as explained by the set of independent variable included in the model.

So, the proportion of observed variation in mist that can be attributed to the simple linear regression relationship between velocity and mist is: 0.929.

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(c) Slope coefficient of a variable tells us about the amount by which dependent variable would increase on an average with a unit increase in that independent variable.

So, the true average change in mist associated with 1cm/sec increase in velocity would be the 95% confidence interval of slope which can be obtained from output as -

(0.000375, 0.000723)

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