Professor Gill has taught General Psychology for many years. During the semester, she gives three multiple-choice exams, each worth 100 points. At the end of the course, Dr. Gill gives a comprehensive final worth 200 points. Let x,, x2, and X, represent a student's scores on exams 1, 2, and 3, respectively. Let x4 represent the student's score on the final exam. Last semester Dr. Gill had 25 students in her class. The student exam scores are shown below. X1 73 93 X2 80 88 Xз X4 75 152 93 185 89 96 91 90 180 98 100 196 73 66 70 142 53 46 55 101 69 74 77 149 47 56 60 115 87 79 90 175 79 70 88 164 69 70 73 141 70 65 74 141 93 95 91 184 SH 79 80 73 152 7. 70 73 78 148 93 89 192 96 68 78 75 147 81 90 93 183 88 92 86 177 78 83 77 159 82 86 90 177 86 82 89 175 78 83 85 175 76 83 71 149 96 93 95 192 Since Professor Gill has not changed the course much from last semester to the present semester, the preceding data should be useful for constructing a regression model that describes this semester as well. БH
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
(e) If a student were to study "extra hard" for exam 3 and increase his or her score on that exam by 14 points, what corresponding change would you expect on the final exam? (Assume that exams 1 and 2 remain "fixed" in their scores.) (Use 1 decimal place.)
Test each coefficient in the regression equation to determine if it is zero or not zero. Use level of significance 5%. (Use 2 decimal places for t and 3 decimal places for the P-value.)
| t | P-value | |
| β1 | ||
| β2 | ||
| β3 |
(f) Find a 90% confidence interval for each coefficient. (Use 2 decimal places.)
| lower limit | upper limit | |
| β1 | ||
| β2 | ||
| β3 |
(g) This semester Susan has scores of 68, 72, and 75 on exams 1, 2, and 3, respectively. Make a prediction for Susan's score on the final exam and find a 90% confidence interval for your prediction (if your software supports prediction intervals). (Round all answers to nearest integer.)
| prediction | |
| lower limit | |
| upper limit |
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