Question

r studio answer to these questions

What is the intercept parameter (2dp) for the regression equation of height (y) versus age (x) using the pine_growth.csv data?

What is the total amount of variation explained by the regression model (SSr) of height (y) versus age (x) using the pine_growth.csv data?

What is the residual error sum of squares (SSe) of a regression model of height (y) versus age (x) using the pine_growth.csv data.

Use your regression equation fitted to the pine_growth.csv data to predict the height (1 dp) of pine trees at 21.8 years.

pine_growth.csv

age   height
7.15576656   18.72849431
8.129775638   35.65477778
16.72602077   40.84925353
22.1494314   61.16668286
24.98842629   63.88029087
10.84800989   38.8948113
16.21167696   50.89108137
21.62648568   58.84822993
27.37032481   58.21976844
8.781800332   38.78419079
15.73044358   47.08995523
18.44298031   47.03292591
24.55722077   57.78373702
8.803465152   19.78892211
14.69364295   38.47185166
19.76821622   52.85251645
25.73732976   54.03867394
9.557438738   19.52645519
13.38045294   50.71181575
21.18576248   50.32075486
25.14524863   66.45636737
11.05895289   35.09854872
15.90885155   46.20593357
21.16517367   59.1335112
24.74997389   53.78095766
10.76039501   31.87024304
17.24982036   38.43437782
20.67469663   42.75693936
24.9187064   56.50248257
9.456849174   27.94407215
17.31785455   44.56102526
19.4035485   43.26457601
26.94362485   69.07639749
10.18743471   30.07622452
14.82076927   32.81933238
19.41960951   45.6665625
26.22703124   54.85557574
11.19384358   37.97390848
13.43821684   44.08033847
20.28160916   60.39976036
26.66076684   66.07282947
10.75153533   27.48342127
15.10263364   30.26795241
19.30307787   47.03971079
26.1097938   57.30252533
7.334193884   16.02310563
7.780802556   29.81303216
13.55907716   35.60521517
18.98254692   45.67647822
27.2336165   49.5956103
8.64498995   22.56785223
16.72757792   40.15677105
18.76667604   39.37013143
26.03969617   62.91864072
11.89543801   16.12208671
14.86010339   33.6554498
18.36353229   50.36578767
25.28054491   65.29231743

Answer 1

1)the intercept is 10.255

2)r square is 0.7712. So, 77.12% of the total variability is explained by the regression model

3) SSRes=2506.3

4)x=21.8, predicted y= 10.255+1.946*21.8=52.6778

r code I used and results:

fit=lm(y~x)

fit

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept) x  
10.255 1.946

> summary(fit)

Call:
lm(formula = y ~ x)

Residuals:
Min 1Q Median 3Q Max
-17.2883 -5.1722 -0.5533 5.6190 14.4112

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10.2548 2.6176 3.918 0.000246 ***
x 1.9464 0.1417 13.740 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.69 on 56 degrees of freedom
Multiple R-squared: 0.7712,   Adjusted R-squared: 0.7671
F-statistic: 188.8 on 1 and 56 DF, p-value: < 2.2e-16

anova(fit)
Analysis of Variance Table

Response: y
Df Sum Sq Mean Sq F value Pr(>F)
x 1 8448.8 8448.8 188.78 < 2.2e-16 ***
Residuals 56 2506.3 44.8
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>

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