A graduate teaching assistant for an Introduction to Statistics course collected data from one of her classes to investigate the relationship between using the explanatory variable x=study time per week (average number of hours) to predict the response variable y=college GPA. For the 21 females in her class, the correlation was 0.42. For the eight males in her class, the data were as shown in the following table. Complete parts a through c below. Student 1 2 3 4 5 6 7 8 Study Time 15 6 22 13 24 4 10 15 GPA 3.4 2.8 3.9 3.2 3.7 2.7 3.2 2.7 a. Construct a scatterplot. Interpret. Which scatterplot below correctly shows the data? A. 04004xy A scatterplot has a horizontal x-axis labeled from 0 to 40 in increments of 10 and a vertical y-axis labeled from 0 to 4 in increments of 1. A cluster of plotted points that form a line that rises from left to right lie between horizontal coordinates of 0 and 30 and the vertical coordinates of 2 and 4. The cluster includes (2.7, 4), (2.7, 15), and (2.8, 6). Your answer is correct. B. 04004xy A scatterplot has a horizontal x-axis labeled from 0 to 40 in increments of 10 and a vertical y-axis labeled from 0 to 4 in increments of 1. A cluster of plotted points that form a line that falls from left to right lie between horizontal coordinates of 0 and 30 and the vertical coordinates of 2 and 4. The cluster includes (10, 2.7), (24, 3.2), and (15, 3.9). C. 04004xy A scatterplot has a horizontal x-axis labeled from 0 to 40 in increments of 10 and a vertical y-axis labeled from 0 to 4 in increments of 1. A cluster of plotted points that form a line that falls from left to right lie between horizontal coordinates of 0 and 30 and the vertical coordinates of 2 and 4. The cluster includes (4, 3.7), (10, 2.8), and (15, 3.9). D. 04004xy A scatterplot has a horizontal x-axis labeled from 0 to 40 in increments of 10 and a vertical y-axis labeled from 0 to 4 in increments of 1. A cluster of plotted points that form a line that falls from left to right lie between horizontal coordinates of 0 and 30 and the vertical coordinates of 2 and 4. The cluster includes (10, 3.2), (24, 2.8), and (22, 3.9). The scatterplot shows a strong positive association between the two variables. b. Find and interpret the correlation. The correlation is 0.830.83. (Round to two decimal places as needed.) The correlation shows a strong positive association between the two variables, with longer study times associated with higher GPAs. c. Find and interpret the prediction equation by reporting the predicted GPA for a student who studies (i) 9 hours per week, (ii) 24 hours per week. The regression equation is y=nothing+x. (Round to two decimal places as needed.) Enter your answer in the edit fields and then click Check Answer.
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.
Student
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
|
---|---|---|---|---|---|---|---|---|---|
Study Time
|
15
|
6
|
22
|
13
|
24
|
4
|
10
|
15
|
|
GPA
|
3.4
|
2.8
|
3.9
|
3.2
|
3.7
|
2.7
|
3.2
|
2.7
|
|
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a.
In this case, the independent variable is study time per week (x) and the dependent variable is college GPA (y).
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