(a)The following table shows the amount of melted plastic (in grams) at various temperatures of the plastic (in Celsius). Temperature (Celcius) 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Melted Plastic (in grams) 8.1 7.8 8.5 9.8 9.5 8.9 8.6 10.2 9.3 9.2 10.5 (I)Find the linear regression equation of the amount of melted plastic temperature. (ii)Estimate the amount of melted plastic at temperature 1.75 Celcius. (iii)Calculate the coefficient of correlation and comment on the relationship between temperature and amount of melted plastic. (iv)Calculate the Spearman’s rank correlation coefficient for the above data
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.
(a)The following table shows the amount of melted plastic (in grams) at various temperatures of the plastic (in Celsius).
|
Temperature (Celcius) |
1.0 |
1.1 |
1.2 |
1.3 |
1.4 |
1.5 |
1.6 |
1.7 |
1.8 |
1.9 |
2.0 |
|
Melted Plastic (in grams) |
8.1 |
7.8 |
8.5 |
9.8 |
9.5 |
8.9 |
8.6 |
10.2 |
9.3 |
9.2 |
10.5 |
(I)Find the linear regression equation of the amount of melted plastic temperature.
(ii)Estimate the amount of melted plastic at temperature 1.75 Celcius.
(iii)Calculate the coefficient of
(iv)Calculate the
(b)A random sample of twelve students were chosen, and their midterm test score ( y), assignment score (x1), and missed classes (x2) were recorded as follows:
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(i)What is the fitted multiple linear regression equation of the form ˆy = b0 + b1x1 + b2x2?
(ii)From part 6(b)(i) above, estimate the midterm test score grade for a student who has an assignment score of 60 and missed 4 classes.
(iii)Assume that the data on ( y, x1, x2) above in 6(b) is inputted into SPSS, with the following results:
|
|
A. At a 5% level of significance, test whether the individual variables, assignment score (x1) and missed classes (x2) are significant explanatory variables for the midterm test score.
B. Find the constants a,b,c,d,e,f, and g in the ANOVA table
C. Test the overall significance of the multiple linear regression model/equation in (I) at a 1% level of significance.
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