Please use R-studios (AND ONLY R-STUDIO) and i also need a step by step of how y
ID: 3320729 • Letter: P
Question
Please use R-studios (AND ONLY R-STUDIO) and i also need a step by step of how you got the answer. The following data are for intelligence-test (IT) scores, reading rates (RR), and grade-point averages (GPA) of 8 at-risk students. IT 184 202 202 167 202 210 199 181 RR 34 30 42 34 22 45 22 25 GPA||2.4 | 1.812.012.3] 1.813.1 || 1.7[20 Part a: Calculate the line of best fit that predicts the GPA on the basis of RR scores. Part b: Calculate the line of best fit that predicts the GPA on the basis of IT scores. Part c: Which of the two lines calculated in parts a and b best fits the data? Justify your answer.
Explanation / Answer
> IT=c(184,202,202,167,202,210,199,181)
> RR=c(34,30,42,34,22,45,22,25)
> GPA=c(2.4,1.8,2.9,2.3,1.8,3.1,1.7,2.0)
> ##(a)
> fit1=lm(GPA~IT)
> fit1
Call:
lm(formula = GPA ~ IT)
Coefficients:
(Intercept) IT
1.031423 0.006302
> summary(fit1)
Call:
lm(formula = GPA ~ IT)
Residuals:
Min 1Q Median 3Q Max
-0.58545 -0.50435 0.01853 0.31107 0.74524
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.031423 2.833475 0.364 0.728
IT 0.006302 0.014617 0.431 0.681
Residual standard error: 0.56 on 6 degrees of freedom
Multiple R-squared: 0.03005, Adjusted R-squared: -0.1316
F-statistic: 0.1859 on 1 and 6 DF, p-value: 0.6814
> anova(fit1)
Analysis of Variance Table
Response: GPA
Df Sum Sq Mean Sq F value Pr(>F)
IT 1 0.05829 0.05829 0.1859 0.6814
Residuals 6 1.88171 0.31362
> ##(b)
> fit2=lm(GPA~RR)
> fit2
Call:
lm(formula = GPA ~ RR)
Coefficients:
(Intercept) RR
0.41516 0.05779
> summary(fit2)
Call:
lm(formula = GPA ~ RR)
Residuals:
Min 1Q Median 3Q Max
-0.34887 -0.00992 0.03881 0.09157 0.14008
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.41516 0.24089 1.723 0.135583
RR 0.05779 0.00735 7.863 0.000224 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1691 on 6 degrees of freedom
Multiple R-squared: 0.9115, Adjusted R-squared: 0.8968
F-statistic: 61.83 on 1 and 6 DF, p-value: 0.0002239
> anova(fit2)
Analysis of Variance Table
Response: GPA
Df Sum Sq Mean Sq F value Pr(>F)
RR 1 1.76839 1.7684 61.826 0.0002239 ***
Residuals 6 0.17161 0.0286
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
##(c)
For model 1 R^2 is 0.03005 and for model 2 is 0.9115 which is greater than model 1 ,so model 2 is best fit.