Question

Consider the data set:

L T    0.5 1.915684 0.7 1.29032 0.9 1.90683 1.1 1.840219 1.3 2.668192 1.5 2.432488 1.7 2.91615 1.9 2.731426 2.1 2.659927 2.3 2.662569 2.5 2.847514 2.7 3.754418 2.9 3.675227 3.1 3.363444 3.3 3.377861 3.5 4.080403 3.7 4.38519 3.9 4.073612 4.1 4.356581 4.3 4.27699

For this data we do not know how T depends on L. We hope that T is proportional to some power of L. Transform data by taking Logarithms and do linear regression. Upon computing the regression round to one decimal.

1.What is the slope?

2.What is R²? Use two decimals

3.Predict the value of T when L = 4.7 Use one decimal

Answer 1

Result:

For this data we do not know how T depends on L. We hope that T is proportional to some power of L. Transform data by taking Logarithms and do linear regression. Upon computing the regression round to one decimal.

1.What is the slope?

Slope=3.1674

2.What is R2? Use two decimals

R square = 0.8432

84.32% of variance in T is explained by regression.

3.Predict the value of T when L = 4.7 Use one decimal

The regression line is T= 2.0671+3.1674*log(L)

When L= 4.7

Predicted T = 2.0671+3.1674*log(4.7) =4.195902755

= 4.2 ( one decimal)

Excel used for calculations:

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Regression Analysis.

Regression Analysis
	r²	0.8432	n	20
	r	0.9183	k	1
	Std. Error of Estimate	0.3772	Dep. Var.	T
Regression output					confidence interval
variables		coefficients	std. error	t (df=18)	p-value	95% lower	95% upper
Intercept	a =	2.0671	0.132	15.710	0.0000	1.791	2.344
logL	b =	3.1674	0.322	9.840	0.0000	2.491	3.844
ANOVA table
Source	SS	df	MS	F	p-value
Regression	13.777	1	13.777	96.82	0.0000
Residual	2.561	18	0.142
Total	16.339	19