Question

1. 
   The following table shows the hour studied per week and the GPA for 19 students. Complete the table and answer the questions that follow. Study Hours per Week (x) GPA (V) 0.5 1.9 1 2.3 4 2.3 2.4 1.5 2.5 2.5 2.5 2.5 2.5 1.5 2.7 2.7 2.77 2.78 4 2.8 2 2.8 4 2.8 4 2.8 3 2.8 0.25 2.83 |ת| תש| | |ס|| תי|| תט|| Study Hours Z-GPAZ Z-score score score product -1.458 -2.795 4.07511 -1.152 -1.171 1.348992 0.685 -1.171 -0.802135 1.297 -0.765 -0.992205 -0.846 -0.359 0.303714 0.685 -0.359 -0.245915 0.072 -0.359 -0.025848 1.909 -0.359 -0.685331 -0.540 -0.359 0.19386 -0.846 0.453 -0.383238 -0.540 0.453 -0.24462 1.297 0.737 0.955889 -0.540 0.778 -0.42012 0.685 0.859 0.588415 -0.540 0.859 -0.46386 0.685 0.859 0.588415 0.685 0.859 0.588415 0.072 0.859 0.061848 -1.611 0.981 -1.580391 Standard Deviation 1.634 0.246 Mean 2.882 2.588
   

1. Compute the correlation coefficient between GPA and Study Hours using the Z-score products from the table. Show work.
2. Find the slope coefficient for the regression line (assume that GPA (y) is a function of HOURS (x)).
3. Find the intercept for the regression line.
4. Write the regression model.
5. Predict the GPA of someone who studies 10 hours per week.

Please someone help with this. I have my own answers but I believe they're wrong.

Answer 1

> x<-c(0.5,1,4,5,1.5,4,3,6,2,1.5,2,5,2,4,2,4,4,3,0.25)
> y<-c(1.9,2.3,2.3,2.4,2.5,2.5,2.5,2.5,2.5,2.7,2.7,2.77,2.78,2.8,2.8,2.8,2.8,2.8,2.83)

> xs<-(x-mean(x))/sd(x)
> xs
[1] -1.45771418 -1.15167474 0.68456191 1.29664079 -0.84563530 0.68456191 0.07248303 1.90871967 -0.53959586 -0.84563530
[11] -0.53959586 1.29664079 -0.53959586 0.68456191 -0.53959586 0.68456191 0.68456191 0.07248303 -1.61073390
> ys<-c(y-mean(y))/(sd(y))
> ys
[1] -2.7954270 -1.1711728 -1.1711728 -0.7651092 -0.3590457 -0.3590457 -0.3590457 -0.3590457 -0.3590457 0.4530814
[11] 0.4530814 0.7373259 0.7779323 0.8591450 0.8591450 0.8591450 0.8591450 0.8591450 0.9809641
> cor(xs,ys)
[1] 0.1589912

> mod<-lm(y~x)
> summary(mod)

Call:
lm(formula = y ~ x)

Residuals:
Min 1Q Median 3Q Max
-0.6313 -0.1392 0.1308 0.1848 0.3046

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.51936 0.11879 21.208 1.15e-13 ***
x 0.02397 0.03609 0.664 0.516
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2502 on 17 degrees of freedom
Multiple R-squared: 0.02528,   Adjusted R-squared: -0.03206
F-statistic: 0.4409 on 1 and 17 DF, p-value: 0.5156