Linear Regression discussion

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Plot the following data. Fit a straight-line linear regression (trendline) to the following data. Set the intercept at 0 and display the equation. Using the regression result, what concentration should be present at time 14.7? Time 1 3 4 5 6 7 13 14 16 18 20 21 22 23 Conc (mg/L) 9.3 40.3 52.3 46.9 84.9 96.2 153.5 175.3 183.6 162.5 177.9 203.1 211.7 228.6 Time 14.7 Regression equations can be used to smooth noisy data or identify an underlying trend. Find the best fit non-polynomial regression equation for the following data (highest R2) and use it to calculate smoothed data Time 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2 5.4 Smoothed Conc (mg/L) Conc (mg/L) 0.519 0.31 1.509 1.561 1.996 1.234 2.368 2.627 2.331 2.674 2.027 3.146 3.122 2.478 3.413 2.52 2.798 2.974 3.931 3.95 3.249 3.152 4.046 to calculate smoothed data values at each time. Find the best-fit (and most reasonable) regression through the data below. Calculated the sum of residual squares (regression error). Time (m) Velocity (m/s) 0.1 0.01 1 1.93 2 3.26 3 3.82 4 4.27 7 5.03 10 5.72 15 6.14 20 6.99 25 7.33 30 7.02 The table below shows the value of office buildings compared with several criteria. Use the data below to perform a multivariate analysis. On average, how much would you expect the value of the building to increase with 1 additionl office? Using a t-test, are any of the parameter coefficients not significant at the 95% confidence level? Using an F-test, is the predictive analysis significant at the 95% confidence level? How much would you expect an office building to be worth that is 27 years old with 2,410 sq ft of floor space, 2 offices and 2 Floor space Offices Entrances Age $ Value 2,310 2 2 20 141,500 2,333 2 2 12 145,000 2,356 3 1 33 151,000 2,379 3 2 43 150,000 2,402 2 3 53 139,000 2,425 4 2 23 169,000 2,448 2 1 89 126,000 2,471 2 4 34 142,900 2,494 3 3 23 163,000 2,517 4 4 55 169,000 2,540 2 3 22 149,000 Fit a curve exactly through the following points using linear algebra and simultaneous equations. Solve for the coefficients for the x-terms and the intercept. x 1 2 3 4 5 y 2.35 3.66 5.11 4.18 7.81 Use Lagrange interpolating polynomials to interpolate the value of 16.4. for the following four points--use all the points . Interpolated Value x y x y 16.4 11 3.52 15 2.65 18 2.56 25 3.78
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Let the equation be
Y=ax4 +bx3 +cx2 +dx+e
x
1
2
3
4
5

y
2.35
3.66
5.11
4.18
7.81

Now, x=1, y=2.35=>2.35=a+b+c+d+e ----------------1
When, x=2, y=3.66, => 3.66=16a+8b+4c+2d+e -------2
When, x=3, y=5.11, => 5.11=81a+27b+9c+3d+e -------3
When, x=4, y=4.18, => 4.18=256a+64b+16c+4d+e -------4
When, x=5, y=7.81, => 7.81=625a+125b+25c+5d+e -------5
Solve the above five equation, we have
a= 0.3942,b=-4.3167,c=16.386,d=-23.228,e=13.16
Thus the equation is
Y= 0.3942x4 -4.3167x3 +16.386x2 -23.288x+13.16


Plot the following data.
Fit a straight-line linear regression (trendline) to the following data. Set the intercept at 0 and display the equation.
Using the regression result, what concentration should be present at time 14.7?

Time
1
3
4
5
6
7
13
14
16
18
20
21
22
23

Conc (mg/L)
9.3
40.3
52.3
46.9
84.9
96.2
153.5
175.3
183.6
162.5
177.9
203.1
211.7
228.6

Time 14.7
Concentration

149.29

SUMMARY OUTPUT
Regression Statistics
Multiple R
0.992211
R Square
0.984484
Adjusted R Square
0.907561
Standard Error
19.15744
Observations
14
ANOVA
df
Regression
Residual
Total

Intercept
Time

1
13
14

SS
MS
302717.2515 302717.3
4771.098453 367.0076
307488.35

Coefficients
0
10.15581

Sta...


Anonymous
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