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 if the ACT score is increased by five points?
b. Compute the fitted values and residuals for each observation, and verify that the residuals (approximately) sum to zero
c. What is the predicted value of GPA when ACT 20?
d. How much of the variation in GPA for these eight students is explained by ACT? Explain.
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The following table contains ACT scores and the GPA (grade point average) for eight college students.
The following table contains the ACT scores and the GPA for eight college students. Grade point...
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...
4. [35 points] The following table contains the ACT scores and the GPA for ten college...
4. [35 points] The following table contains the ACT scores and the GPA for ten college students. Student GPA ACT 2.821 3.4 24 3.026 3.5 27 3.629 3.025 3.225 3.5 28 2.520 3.7 30 10 (a) [10 points] Estimate the relationship between GPA and ACT; that is, obtain the intercept and slope estimates in the equation (You may use a calculator or a spreadsheet program, but show your work.) (b) [2 points] Does the intercept have a useful interpretation here?...
The following table contains the ACT scores and the GPA (grade point average) for three college...
The following table contains the ACT scores and the GPA (grade point average) for three college students. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal. Estimate the relationship between GPA and ACT using OLS. Consider the slope estimate (beta1_hat) in equation GPA_hat=beta0_hat+beta1_hat*ACT. Is the relationship between GAP and ACT positive or negative? Student GPA ACT 1 2.8 21 2 3.4 24 3 3.0 26
Grade point average. The director of admissions of a small college seleeted 120 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.....
2. . In a study relating college grade point average (GPA) to time spent in various...
2. . In a study relating college grade point average (GPA) to time spent in various activities, you distribute a survey to several students. The students are asked how many hours they spend each week in four activities: studying, sleeping, working, and leisure. Any activity is put into one of the four categories, so that for each student, the sum of hours in the four activities must be 168. Based on the study, you set an econometric model: GPA P+study+B,sleep+,work+B,leisure+...
It is believed that average grade (based on a four-point scale) should have a positive linear...
It is believed that average grade (based on a four-point scale) should have a positive linear relationship with university entrance exam scores. Given below is the Microsoft Excel output from regressing average grade on university entrance exam scores using a data set of eight randomly chosen students from a large university. Coefficients Standard Error 0.5681 0.9284 1 Stat 0.6119 P-value 0.5630 Lower 95% -1.7036 Upper 95% 2.8398 Intercept University entrance exam score 0.1021 0.0356 2.8633 0.0286 0.0148 0.1895 If we...
A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n15 college students
A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n15 college students. The SAT scores have a mean of M = 580 with SS 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84. Find the regression equation for predicting GPA from SAT scores. (Use five decimal places for the slope.)
C. Calculation Problems (40 marks) 1. Using the data in GPA2.RAW on 4,137 college students, the...
C. Calculation Problems (40 marks) 1. Using the data in GPA2.RAW on 4,137 college students, the following equation was esti- mated by OLS: colgpa = 1.392 - 0135 hsperc+.00148 sat n =4,137, R2 = 273, where colgpa is measured on a four-point scale, hsperc is the percentile in the high school graduating class (defined so that, for example, hsperc =5 means the top 5% of the class), and sat is the combined math and verbal scores on the student achievement...
A statistics professor classifies his students according to their grade point average (GPA) and their class...
A statistics professor classifies his students according to their grade point average (GPA) and their class rank. GPA is on a 0.0 - 4.0 scale and class rank is defined as the under" dass (freshmen and sophomores) and the upper class (Juniors and seniors). One student is selected at random GPA Class Under 2.0 2.0 - 3.0 Upper 0.117 0.207 Under 0.338 0.090 Given the student selected is in the "Under" class, what is the probability that her GPA is...
Alatistics professor classifies his students according to their grade point average (GPA) and their class rank....
Alatistics professor classifies his students according to their grade point average (GPA) and their class rank. GPA is on a 0.0-4.0 scale and class rank is defined as the under class of eshmen and sophomorest and the upper class unitors and seniors One student is selected at random Class Upper Under Under 2.0 0.117 0.338 GPA 20.30 0207 0.000 Over 10 0.145 0.103 What is the probability that the student is in the upper class and has GPA under 2.0?...
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...
4. [35 points] The following table contains the ACT scores and the GPA for ten college students. Student GPA ACT 2.821 3.4 24 3.026 3.5 27 3.629 3.025 3.225 3.5 28 2.520 3.7 30 10 (a) [10 points] Estimate the relationship between GPA and ACT; that is, obtain the intercept and slope estimates in the equation (You may use a calculator or a spreadsheet program, but show your work.) (b) [2 points] Does the intercept have a useful interpretation here?...
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.....
2. . In a study relating college grade point average (GPA) to time spent in various activities, you distribute a survey to several students. The students are asked how many hours they spend each week in four activities: studying, sleeping, working, and leisure. Any activity is put into one of the four categories, so that for each student, the sum of hours in the four activities must be 168. Based on the study, you set an econometric model: GPA P+study+B,sleep+,work+B,leisure+...
It is believed that average grade (based on a four-point scale) should have a positive linear relationship with university entrance exam scores. Given below is the Microsoft Excel output from regressing average grade on university entrance exam scores using a data set of eight randomly chosen students from a large university. Coefficients Standard Error 0.5681 0.9284 1 Stat 0.6119 P-value 0.5630 Lower 95% -1.7036 Upper 95% 2.8398 Intercept University entrance exam score 0.1021 0.0356 2.8633 0.0286 0.0148 0.1895 If we...
A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n15 college students. The SAT scores have a mean of M = 580 with SS 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84. Find the regression equation for predicting GPA from SAT scores. (Use five decimal places for the slope.)
C. Calculation Problems (40 marks) 1. Using the data in GPA2.RAW on 4,137 college students, the following equation was esti- mated by OLS: colgpa = 1.392 - 0135 hsperc+.00148 sat n =4,137, R2 = 273, where colgpa is measured on a four-point scale, hsperc is the percentile in the high school graduating class (defined so that, for example, hsperc =5 means the top 5% of the class), and sat is the combined math and verbal scores on the student achievement...
A statistics professor classifies his students according to their grade point average (GPA) and their class rank. GPA is on a 0.0 - 4.0 scale and class rank is defined as the under" dass (freshmen and sophomores) and the upper class (Juniors and seniors). One student is selected at random GPA Class Under 2.0 2.0 - 3.0 Upper 0.117 0.207 Under 0.338 0.090 Given the student selected is in the "Under" class, what is the probability that her GPA is...
Alatistics professor classifies his students according to their grade point average (GPA) and their class rank. GPA is on a 0.0-4.0 scale and class rank is defined as the under class of eshmen and sophomorest and the upper class unitors and seniors One student is selected at random Class Upper Under Under 2.0 0.117 0.338 GPA 20.30 0207 0.000 Over 10 0.145 0.103 What is the probability that the student is in the upper class and has GPA under 2.0?...
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