Question

HW 9: Linear Regression and Correlation Analysis

INSTRUCTIONS: Please modify the Excel sheet attached to complete this assignment. Turn in the following work including: 1) written formulas, 2) values from Excel plugged into formulas, and 3) final answer.

Scenario: A graduate student has administered a pro-inflammatory substance, lipopolysaccharide (LPS), to rats in the form of a pill (several doses – 0 mg or placebo, 1.25 mg, 2.5 mg, 5.0 mg, and 10 mg). She then determines the blood concentration of a particular protein that is thought to be upregulated due to LPS called Inflammo using ELISA. Find the linear model and the correlation coefficient of the experimental data on Blackboard labeled “HW9 Raw Data”.

LPS delivered (mg)	Inflammo (ug/mL)
10	2.234
5	1.198
2.5	0.735
1.25	0.411
0	0.105
10	2.337
5	1.201
2.5	0.805
1.25	0.431
0	0.088
10	2.115
5	1.275
2.5	0.881
1.25	0.249
0	0.101
10	2.176
5	1.303
2.5	0.691
1.25	0.383
0	0.089

(10pts)Equation for Linear Model:

(10pts)Correlation Coefficient:

(10pts)Does the linear model describe the relationship between LPS and Inflammotin concentration well?

(10pts)If so, what type of correlation exists between LPS dosage and Inflammo concentration?

Equations/formulas (30 pts)(Attach work):

Answer 1

we will perform analysis using excel and steps are

1) Enter data into excel

2) click on Data tab Then click On Data Analysis select Regression

Now in output range select dependent variable that is Inflammo (ug/mL

and for input range select range of LPS delivered (mg)

click on labels if your selecting data including labels.

click on ok

It will give following output

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9933
R Square	0.9866
Adjusted R Square	0.9858
Standard Error	0.0915
Observations	20.0000
ANOVA
	df	SS	MS	F	Significance F
Regression	1.0000	11.0660	11.0660	1321.8489	0.0000
Residual	18.0000	0.1507	0.0084
Total	19.0000	11.2167
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0.1514	0.0298	5.0777	0.0001	0.0888	0.2141
LPS delivered (mg)	0.2104	0.0058	36.3572	0.0000	0.1982	0.2225

Equation for Linear Model

Inflammo (ug/mL) =0.1514+0.2104*LPS delivered (mg)

Correlation Coefficient:  0.9933

Does the linear model describe the relationship between LPS and Inflammotin concentration well?

From Anova table

p-value = 0 < 0.05 level of significance so we reject the null hypothesis and conclude that relationship between LPS and Inflammotin concentration is significant.

If so, what type of correlation exists between LPS dosage and Inflammo concentration

Correlation Coefficient:  0.9933

so their is perfect positive correlation between LPS dosage and Inflammo concentration