An education researcher wants to explore the relationship between the grades stu

Question

An education researcher wants to explore the relationship between the grades students receive on their First test and their Final test score in a graduate level statistics class. The following data present the First test and Final test scores for ten students. The data set is listed below: [Use R and provide the R code in support of your answer. Also, provide all the details wherever necessary for full credit.]

First Test score and (Final test score): 182 (285) 193 (268) 217 (310) 205 (319) 226 (334) 245 (355) 265 (372) 268 (323) 266 (407) 270 (356).

6). Verify that sum of the residuals is indeed zero. [Just provide the R-code here]

7). Compute 90% confidence interval for the slope (1) coefficient. Can you perform a test of hypothesis H0 : 1 = 0 against H1 : 1 = 0 based on your computed confidence interval? Explain. Also, interpret the computed interval.

8). Provide the estimated value of the mean function E(Yh) for Xh = 187. Also, compute the estimated variance for the mean function at this particular value of Xh.

Explanation / Answer

first=c(182,193,217,205,226,245,265,268,266,270)
final=c(285,268,310,319,334,355,372,323,407,356)

fit=lm(final~first)

e=resid(fit)
sum(e) # is very near to 0

confint(fit,level=0.90)

newobs=96.419+1.012*187
newobs

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