View the step-by-step solution to:

Question

A. Find the 95%confidence interval forβ1 was(.014,.064), and thus concluded that there is a positive association

between X and Y in the population. To form the confidence interval, you used the R output for the standard error ofˆβ1(.01277). Now, verify this standard error using the formula given in class for SD(ˆβ1).


B Carry out the hypothesis test of the null hypothesis that there is no association between X and Y. State the hypotheses in appropriate notation, report the value of the test statistic and the P-value, and state your conclusion.


C Consider individuals whose ACT test score is 28. (i) Obtain the value ofˆY for such individuals. (ii) Obtain the value of the standard error ofˆY


D Obtain a 95%confidence interval for the mean freshman GPA for students whose ACT test score is 28.Interpret the confidence interval.


E Show the ANOVA table. Report R2; interpret its value.


For this,


Here is summary


Call:

lm(formula = gpa ~ act, data = gpa.df)


Residuals:

   Min    1Q  Median    3Q   Max 

-2.74004 -0.33827 0.04062 0.44064 1.22737 


Coefficients:

      Estimate Std. Error t value Pr(>|t|)   

(Intercept) 2.11405  0.32089  6.588 1.3e-09 ***

act     0.03883  0.01277  3.040 0.00292 ** 

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 0.6231 on 118 degrees of freedom

Multiple R-squared: 0.07262, Adjusted R-squared: 0.06476 

F-statistic: 9.24 on 1 and 118 DF, p-value: 0.002917



Mean [1] 24.725

SD [1] 4.472065




$fit

    fit    lwr    upr

1 3.201209 3.061384 3.341033


$se.fit

[1] 0.07060873


$df

[1] 118


$residual.scale

[1] 0.623125




Anova table.

Response: gpa

       Df Sum Sq Mean Sq F value   Pr(>F)  

act      1  3.588  3.5878  9.2402 0.002917 **

Residuals 118 45.818  0.3883           

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Recently Asked Questions

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question
Ask Expert Tutors You can ask You can ask ( soon) You can ask (will expire )
Answers in as fast as 15 minutes