'Suppose local university researcher wants to build linear model that predicts the freshman year GPA of incoming students based on high school SAT scores. The researcher randomly selects sample of 40 sophomore students at the university and gathers their freshman year GPA data and the high school SAT score reported on each of their college applications He produces a scatterplot with SAT scores On the horizontal axis and GPA on the vertical axis. The data has linear correlation coefficient of 0.454012. Additional sample statistics are summarized in the table below: Variable Sample Sample standard Variable description mean deviation high school SAT score x =1503.578103 Sx = 107.836402 freshman year GPA y = 3.299812 0.517403 r = 0.454012 slope 0.002178 Determine the y-intercept; a, of the least-squares regression line for this data. Give your answer precise to four decimal places. Avoid rounding until the last step.'
Added by Brenda J.
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1. The director of admissions at 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 can be predicted from their ACT test score. The data can be found at "GPA.txt". (a) Fit a simple linear regression using ACT score as the explanatory variable, and GPA as the response variable by computing ̄X, ̄Y and then SXX, SXY and SYY. Use the values of ̄X, ̄Y, SXX, SXY and SYY from (a) to answer the following parts. (b) Estimate the parameter ̴̵̶̷̸̡̢̧̨̛̖̗̘̙̜̝̞̟̠̣̤̥̦̩̪̫̬̭̮̯̰̱̲̳̹̺̻̼͇͈͉͍͎̐̑̒̓̔̽̾̿̀́͂̓̈́͆͊͋͌̕̚ͅ͏͓͔͕͖͙͚͐͑͒͗͛ͣͤͥͦͧͨͩͪͫͬͭͮͯ͘͜͟͢͝͞͠͡ͰͱͲͳʹ͵Ͷͷͺͻͼͽ;Ϳ΄΅Ά·ΈΉΊΌΎΏΐΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩΪΫάέήίΰαβγδεζηθικλμνξοπρςστυφχψωϊϋόύώϏϐϑϒϓϔϕϖϗϘϙϚϛϜϝϞϟϠϡϢϣϤϥϦϧϨϩϪϫϬϭϮϯϰϱϲϳϴϵ϶ϷϸϹϺϻϼϽϾϿσ. (c) Use a t-test to determine whether or not there a linear relationship between ACT score and GPA. (d) Compute the ANOVA table corresponding to the model. (e) From the table determine the mean square error (MSE). (f) Use the ANOVA F-test to determine whether or not there is a linear relationship between ACT score and GPA. (g) How do the results in (e) compare to those in (b)? (h) How do the results in (f) compare to those in (c)? (i) What proportion of the variation in GPA is explained by the regression model?
Dominador T.
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): x 1 = average high school grade in mathematics (HSM) x 2 = average high school grade in science (HSS) x 3 = average high school grade in English (HSE) x 4 = SAT mathematics score (SATM) x 5 = SAT verbal score (SATV) A first-order model was fit to the data with the following results: _____________________________________________________________________ ROOT MSE 0.700 R-SQUARE 0.211 DEP MEAN 4.635 ADJ R-SQ 0.193 a) Test to determine if the model is adequate for predicting GPA. Use α = .01. b )Write the model you want to use (explain why and which independent variables you want to use
Sri K.
Suppose administrators at a large school district decide to institute mandatory study halls at their middle schools in an effort to boost their students' academic performance. After one year, a guidance counselor decides to test whether students' grade point averages (GPAs) have improved compared to the previous school year. The counselor selects a random sample of 40 eighth-graders from throughout the district who were also enrolled in the district for seventh grade. He records their GPAs for grades seven and eight, and for each student, calculates the difference between the two. The counselor's data is summarized in the given table: Variable description Sample mean X7 = 2.64796, X8 = 2.78543, 0.13747 Sample standard deviation = 0.45763, 0.54764, S = 0.34586 Standard error estimate SEn = 0.07236, SEs = 0.08659, SE = 0.05469 Seventh grade GPA, Eighth grade GPA, Difference (8th - 7th) The counselor plans to use this information to conduct a matched-pairs t-test of the null hypothesis Ho: μ = 0 against the alternative hypothesis Hj: μ > 0, where μ is the mean change in students' GPAs after mandatory study halls were instituted. What is the t-statistic for the counselor's test? Round your answer to three decimal places. What is the p-value for the counselor's test? Round your answer to four decimal places.
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