Question

The thickness, t, (mm) was recorded versus absorption, A, (c/s), and the results are shown in the following table. thickness ,t, mm Absorption ,A, c/s 0.2 5500 5 3720 10 2550 20 1320 27.5 720 32.5 480 1) Plot the data on the graph paper. 2) Find the equation that best fits the relationship between thickness and absorption.

Answer 1

use plot function to plot Rcode is

Use R software

Create 2 vectors thickness and absorption.

Fir a linear regression of absorption on thickness.

You will get

thickness <- c( 0.2, 5 ,10 ,20 ,27.5 ,32.5 )
Absorption <- c( 5500, 3720 ,2550 ,1320, 720 ,480 )
plot(thickness,Absorption,col = "brown")
linearregresion <- lm(Absorption~thickness)
summary(linearregresion)

Call:
lm(formula = Absorption ~ thickness)

Residuals:
1 2 3 4 5 6
850.17 -234.90 -681.02 -463.26 22.56 506.44

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4678.78 449.20 10.416 0.00048 ***
thickness -144.78 22.76 -6.362 0.00313 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 654.5 on 4 degrees of freedom
Multiple R-squared: 0.9101,   Adjusted R-squared: 0.8876
F-statistic: 40.47 on 1 and 4 DF, p-value: 0.00313

From the above output: linear regression summary we get regression equation used for predicting absorption based on thickness

solution1:

linear regression is

Absorprtion=4678.78 -144.78*thickness

slope= -144.78

y intercept=4678.78