Calculate correlations; least squares lines, make prediction

See attached Minitab file.

The data set CSDATA contains information about all 224 students who entered a large university in a single year and who planned to major in a computer science. We are interested in predicting GPA (grade point average) after three semesters of college from information available before the student enters college. To do this effectively, we must use several explanatory variables together. This is multiple regression. In this Case Study, You will look at the individual explanatory variables.

A. Correlations. What are the correlations of all the explanatory variables with GPA? Explain why knowing the correlations tell us which variables will best predict GPA in a regression with just one explanatory variable. What are the two best predictor variables? Does your finding seem reasonable for computer science majors?

B. Prediction. Make scatterplots, with the least-squares line added, for GPA versus each of the two best explanatory variables. How well do each of these variables predict GPA? Do these scatterplots contain unusual observations? In what way is each of these observations

The data set CSDATA contains information about all 224 students who entered a large university in a single year and who planned to major in a computer science. We are interested in predicting GPA (grade point average) after three semesters of college from information available before the student enters college. To do this effectively, we must use several explanatory variables together. This is multiple regression. In this Case Study, You will look at the individual explanatory variables. Calculate Correlations; construct least squares lines, make prediction and plots

For a set of data, the total variation or sum of squares for y is SST - 143.0 and the error sum of squares is SSE = 24.0. What proportion of the variation in y is explained by the regression equation?
2. A. Determine the leastsquares regression line and calculate r.
B. What proportion of the variability in steel

Bivariate data for the quantitive variables x and y are given in the table below. These data are plotted in the scatter plot shown next to the table. In the scatter plot, sketch an approximation of the least-squares regression line for the data.
X Y
4.2 6.7
4.6 6.2
4.5 5.5
8.6 3.4
3.6

"The linear regression line is sometimes called the leastsquares line. Why?"
What is the idea of "leastsquares"?
What is the connection between "leastsquares" and linear regression?
Could "leastsquares" and regression be generalized to more complicated cases than lines?

1)Given the regression equation: Y = 1.3479 + 0.3978 X, what is the fitted value (orY ? ) if X = -3?
2) Calculate bo, b1 for the information provide below
X Y
-2 9
0 5
-0.5 7
1 100

The following table shows SAT scores (on the old SAT with only two sections) for a sample of
students.
Math 550 510 300 490 600 570 710 500 570 520 590 470
Verbal 560 490 720 500 590 550 410 510 580 520 490 480
a. Give the equation of the leastsquares regression equation.
b. Make a scatterplot, and graph the LSRL on th

QUESTION A:
Assume that there is a correlation between two variables, X and Y. Based on the information provided below, calculate the correlation coefficient.
X 31,30,32,19,25,22,30,19,18,20
Y 32,30,25,22,20,19,18,17,16,15
QUESTION B:
Find a 90% prediction interval for the individual value of Y if X

In fitting a leastsquares line to n=15 data points, the following quantities were computed: SSxx=55, SSyy=198, SSxy=-88, x-bar=1.3, and y-bar=35.
a.) Find the leastsquares line.
b.) Describe the graph of the leastsquares line.
c.) Calculate SSE
d.) Calculate s^2.

The following data show U.S. production of motor vehicles versus tons of domestic steel shipped for motor vehicle manufacture.
Year X=U.S. Production of Motor Vehicles Y=Tons of Domestic Steel
2000 12.83 million 16.06 million
2001 11.52 14.06
2002 12.33 14.0
2003 12.15 15.88
2004 12.02 13.86
a. Determine the least-squar

I'm trying to calculate the sum of squares for errors (SSE) manually and I was given an example with the answer below, but I cannot figure out how they got the answer. Can you please show, or tell me how they got the answer (20) and what +...+ means between these numbers, because each time I calculate, it comes up to 18 and not