Question

Pen Problem Chapter 4 Pen Problem - Chapter 4: Residual Plots Quercetin, a plant flavinoid, is being studied for its potential nutritional and antioxidant properties. The following data was collected in a spectrophometric analysis of tablets containing queretin. Quercetin per tablet (mg) Absorbance 410 0.40 420 0.45 440 0.55 450 0.60 500 1.00 A linear regression analysis of the data produced the following information: Slope = 0.0067 Intercept = -2.4 Correlation (1) - 0.99 (A) Does this value of provide confidence that a straight line is the line of best-fit? Justify your choice by comparing this value to the 99% confidence value in Table 4.9. Table 4.9 value conclusion (B) Using the slope and intercept prepare a data table of the calculated values of absorbance. Calculated absorbance for 410 mg Calculated absorbance for 420 mg - Calculated absorbance for 440 mg = Calculated absorbance for 450 mg = Calculated absorbance for 500 mg = Determine the residual value for each point: Residual for 410 mg Residual for 420 mg = Residual for 440 mg = Residual for 450 mg = Residual for 500 mg = (D) Prepare a graph, including a zero reference line, of residual value on the y-axis and mg of quercetin on the x-axis. (1) Does the graph appear to have random fluctuations or is there a non- random pattern? (Note, Figure 4.13 provides visual examples of both.) (2) What conclusion can be made concerning the line of best-fit for this data?

Answer 1

Sol;
Install analysis toolpak and then go to

Data >Data analysis >Regression you get

Output:

CHOLDATA - Excel venkatnaveen adabala - Go File Home Insert O X & Share Page Layout Formulas Data Review View Help Clear nections A Tell me what you want to do 2 Flash Fill L. Remove Duplicates ? X idation Data Analysis Reanal -- Consolidate Relationships a Show Queries From Table New Query-Lo Recent Sources Get & Transform 3 Get External Data Refresh Prenerties Regression é Group Ungroup E Subtotal Outline All What-If Forecast Analysis Sheet Forecast El Conne Input OK D Data Tools Analysis Input Y Range: $B$1:$B$6 fx quercetin Cancel ✓ C Input X Range: $A$1:$A$6 D Help M N O I e R S T - X A B quercetin Absorban be 0.4 420 440 Labels Confidence Level: Constant is Zero 95 % 410 0.45 450 500 Output options O Output Range: New Worksheet Ply: O New Workbook Residuals Residuals Standardized Residuals Residual Plots Line Fit Plots Normal Probability Normal Probability Plots Sheet1 Sheet3 Sheet4 + ROSE www.youtube.com • 19m ఈశ్వర దండకం ప్రతిరోజు వినడం ... Recommended: Rose Telugu Movies E- - + 100% 13:17 O AO ») ENG 14 11-11-20192 Ready 1 Type here to search e e 9 W Ⓡ SÅ

Multiple R	0.991836598
R Square	0.983739837
Adjusted R Square	0.978319783
Standard Error	0.034921515
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.221341	0.221341463	181.5	0.000884
Residual	3	0.003659	0.001219512
Total	4	0.225
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%
Intercept	-2.37804878	0.221603	-10.73114534	0.00173	-3.08329	-1.67281	-3.08329
quercetin	0.006707317	0.000498	13.47219359	0.000884	0.005123	0.008292	0.005123
RESIDUAL OUTPUT
Observation	Predicted Absorbance	Residuals
1	0.37195122	0.028049
2	0.43902439	0.010976
3	0.573170732	-0.02317
4	0.640243902	-0.04024
5	0.975609756	0.02439

quercetin Residual Plot 0.04 0.02 Residuals -0.020 100 200 300 400 500 600 quercetin

y=-2.4+0.00678x

calculated abosrbance for x=410

substute in regression

y=-2.4+0.00678*410

y= 0.347

Residual=observed y-predicted y

=0.4- 0.347

=0.053

We can directly get this from excel for x=410,420,440,450,500

RESIDUAL OUTPUT
Observation	Predicted Absorbance	Residuals
410	0.37195122	0.028049
420	0.43902439	0.010976
440	0.573170732	-0.02317
450	0.640243902	-0.04024
500	0.975609756	0.02439

calculated absorbance for x=410 is 0.37195122

so calculated absorbance for x=420 is 0.43902439

so calculated absorbance for x=440 is 0.573170732

so calculated absorbance for x=450 is 0.640243902

so calculated absorbance for x=500is 0.975609756

Residual for 410 mg=0.028049

Residual for 420 mg=0.010976

Residual for 440 mg=-0.02317

Residual for 450 mg=-0.04024

Residual for 500 mg=0.02439

From residual plot we observe non random pattern.
Equality of variance assumption is satisfied

R sq=

0.983739837

=98.37% variation in absorbance is explained by quercetin

Good model

Also

From F test

F=181.5

p=0.000884

p<0.05

Model is significant

we can use this model for predicting absorbance