Question

Find the (a) explained variation, (b) unexplained variation, (c) total variation, (d) coefficient of determination, and (e) standard error of estimate sese.

The following table lists numbers xx of patio tiles and costs yy (in dollars) of having them manually cut to fit.

NASA's Land ground measurements of snow depth along with corresponding temperatures

Temperature (in ºC)	Snow depth (in cm)
-62	21
-41	13
-36	12
-26	3
-33	6
-56	22
-50	14
-66	19

(a) explained variation (if necessary, round the the nearest hundredth): Answer

(b) unexplained variation (if necessary, round the the nearest hundredth): Answer

(c) total variation (if necessary, round the the nearest hundredth): Answer

(d) coefficient of determination (if necessary, round the the nearest tenth): Answer

(e) standard error of estimate sese (if necessary, round the the nearest tenth): Answer

Answer 1

Here you didn't mention the independent variable or dependent variable. So, I'm taking Temperature as dependent variable and Snow depth as independent variable.

[Now if you take the opposite case please let me know in the comment, I'll provide you the updated results.]

Using R codes we can easily have the answers.

CODE:

x <- c(21,13,12,3,6,22,14,19)
y <- c(-62,-41,-36,-26,-33,-56,-50,-66)
summary(aov(lm(y~x)))
summary(lm(y~x))

OUTPUT:

> x <- c(21,13,12,3,6,22,14,19)
> y <- c(-62,-41,-36,-26,-33,-56,-50,-66)
> summary(aov(lm(y~x)))
Df Sum Sq Mean Sq F value Pr(>F)
x 1 1256.6 1256.6 36.08 0.000959 ***
Residuals 6 208.9 34.8   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> summary(lm(y~x))

Call:
lm(formula = y ~ x)

Residuals:
Min 1Q Median 3Q Max
-9.466 -2.263 -1.178 4.438 6.822

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -19.3168 4.9454 -3.906 0.007928 **
x -1.9588 0.3261 -6.007 0.000959 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 5.901 on 6 degrees of freedom
Multiple R-squared: 0.8574,   Adjusted R-squared: 0.8337
F-statistic: 36.08 on 1 and 6 DF, p-value: 0.0009587

(a) Explained variation = 1256.6

(b) Unexplained variation = 208.9

(c) Total variation = 1256.6 + 208.9 = 1465.5

(d) Coefficient of determination = 0.9

(e) Stadard error of estimate = 5.9