Let us suppose that ACT test score is denoted with X and is treated as independent variable
and GPA is denoted with Y and is treated as dependent variable
a. From the given data sum of X= 269 sumof squares of X =7333
Sum Of Y = 31.812 Sum of squares of Y = 101.633
Sum of the product of X and Y = 856.726
Mean of X = X-- = 26.9 Mean of Y = Y-- = 3.1812
S.D of X = x= 3.1129 S.D of Y = y= 0.2080
covariance between X and y = 0.09832
Correlation coefficient between X and Y = r= 0.1518
Regression coefficient of Yon X = Beta coefficient =B= 0.010147
Regression equation of Yon X is given as (Y - mean of Y ) = B ( X- mean 0f X)
(Y- 3.1812) = 0.010147( X- 26.9)
Y= 0.010147X + 2.90825
b.compute the residual standard deviation
residual standard deviation = residual sum of square /n-1 =0.4226/9 =0.2166
c. point and interval estimate of intercept and slope
point estimate of slope = B = 0.010147 and intercept = 2.90825
interval estimate of slope B = B+/- (t xs.e(B)) = 0.010147+/- (2.31x0.07553
=(-0.1643, 0.1846)
Interval estimate of intercept = 2.90825+/- 0.5309 = (2.377, 3.43919)
d. test whether ACT test score is associated with GPA
set up H0 ; B = 0 i.e the regession coefficient is not significant
H1 ; B not equal to 0 i.e the regression coefficient is significant it means ACT test score is influencing the GPT
Under H0 the test statistic t= ( Estimated B - 0) /s.e (B) it FOllows t distribution with n-2 d.f
=0.010147/0.0738 = 0.1374
critical value of t for 8 degrees of freedom at 5 % level of significance = 2.31
we observe that t cal value = 0.1374 is less than t tab value = 2.31
hence we accept the null hypothesis i.e the regression coefficient is not significant at 5% level of significance
hence we conclude that ACT test score is not associated with GPA
2. (13 pts.) The director of admissions of a small college selected 10 students at random...
Grade point average. The director of admissions of a small college seleeted 120 students at random from the new freshman class in a study to determine whether a student's grade point average (GPA) at the end of the freshman year (Y) can be predicted from the ACT test score (X) The results of the study follow. Assume that first-order regression model (1.1) is appropriate. 2 118 119 120 i: Xi: 21 Yi: 14 28 28 16 28 3.897 3.885 3.778.....
The direct of admissions of a small college administered a newly designed entrance test to 20 students selected at random from the new freshman class in a study to determine whether a student’s grade point average (GPA) at the end of the freshman year (y) can be predicted from the entrance test score (x). The results are summarized as follows.
Solving (c) would be enough! Thanks a lot! LO LART! 2. (No R required) The director of admissions of a small college selected 120 students at random from the new freshman class in a study to determine whether a student's grade point average (GPA) at the end of the freshman year (y) can be predicted from the ACT test score (x). The director fitted a simple linear regression E(GPA|ACT) = Bo + B1ACT. A lack of fit test was carried...
The admissions officer of Clearwater College developed the following estimated regression equation relating the student's final college grade point average (GPA) to the student's high school grade point average and the student's SAT mathematics score _ _ 1.41 + .0235, + .00486": where v = final college grade point average x-high-school grade point average 2-SAT mathematics score a. Interpret the coefficients in this estimated regression equation There is a .2035 change in high school GPA when there is a 1...
4. The following table contains ACT scores and the GPA (grade point average) for eight college students. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal: a. Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and slope estimates in the equation Comment on the direction of the relationship. Does the intercept have a useful interpretation here? Explain. How much higher is the GPA predicted to be...
The following table contains the ACT scores and the GPA for eight college students. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal. Student GPA ACT 1 2.& 21 2 3.4 24 3 3.0 26 4 3.5 27 5 3.6 29 6 3.0 25 7 2.7 25 8 3.7 30 a) Estimate the relationship between GPA and ACT using OLS: that is, obtain the intercept and slope estimates in the...
please answer all ill leave a good like C The admissions officer for Clearwater College developed the following estimated regression equation relating the final college GPA to the student's SAT O mathematics score and high-school GPA. =-1.4053+.0235z1 +.0049z where high-school grade point average 1 2SAT mathematics score y=final college grade point average Round your answers to 4 decimal places. a. Complete the missing entries in this Excel Regression tool output. Enter negative values as negative numbers. ANOVA df SS MS...
The admissions officer for Clearwater College developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high-school GPA. y = -1.4053 +.023501 +.004932 where 21 = high-school grade point average 22 = SAT mathematics score y = final college grade point average Round your answers to 4 decimal places. a. Complete the missing entries in this Excel Regression tool output. Enter negative values as negative numbers. ANOVA of SS M S F...
The admissions officer for Clearwater College developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high-school GPA. y = -1.4053 +.023541 +.004902 where *1 = high-school grade point average 22 = SAT mathematics score y=final college grade point average Round your answers to 4 decimal places. a. Complete the missing entries in this Excel Regression tool output. Enter negative values as negative numbers. ANOVA of SS M S F Significance F...
The admissions officer for Clearwater College developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high-school GPA. y = -1.4053 +.023571 +.004922 where 21 = high-school grade point average 22 = SAT mathematics score y = final college grade point average Round your answers to 4 decimal places. a. Complete the missing entries in this Excel Regression tool output. Enter negative values as negative numbers. ANOVA SS MS Significance F Regression...