aCalculate the estimates of the slope and y intercept.
bWhat is the regression equation to predict y from x?
cCalculate r and r2.
dAt the 1% level of significance, can you conclude that there is a significant positive correlation between the two variables?
2.A statistics student wonders whether he can predict the annual salary of a first-year employee from their grade point average in a Bachelor of Science (Statistics Major). He obtained data from 10 alumni of his department. The data is given below.
GPA (x)Annual salary ($) (y)
2.740,000
3.243,000
3.649,000
3.345,000
3.148,000
2.536,000
2.739,000
3.342,000
2.930,000
2.622,000
aFind ∑x, ∑y, ∑xy, ∑x2, ∑y2, x ̅y ̅
bUse the summary statistics from part (a) and formulas you may have learned in your previous statistics course OR use the simple linear regression procedures demonstrated in the textbook for this course to obtain the regression equation to predict y from x.
cInterpret the slope and the y intercept with reference to the context.
dWhat is the predicted annual salary of a person with a GPA of 3.6? What is the residual?
eCalculate the coefficient of determination. Use the coefficient of determination to justify whether the model is a good fit.
fUse the test of slope to see whether there is a significant relation between the two variables x and y.
gUse the test of correlation to see whether there is a significant positive correlation coefficient.
hExplain in words why the test statistics for tests (f) and (g), above, are the same.
iConstruct a 95% two-sided confidence interval for slope β.
jConstruct a 95% two-sided confidence interval for correlation coefficient ρ.
3.In a study to determine if response time, y, could be modeled as a linear function of the temperature, a process was run at each of four temperatures three times, a total of twelve pairs of observations. The two AOV tables shown below are (I) for fitting y as a simple linear function of x, and (II) for AOV using the values of x to define the “treatments.”
Analysis of Regression
Sum of Mean
Source DF Squares Square
Regression ______ 290.40000 290.40000
Error ______ 43.60000 4.36000
Total ______ 334.00000
Analysis of Variance
Sum of Mean
Source DF Squares Square
Groups _______ 318.0000000 106.0000000
Error _______ 16.0000000 2.0000000
Total _______ 334.0000000
aComplete the tables by providing the correct degrees of freedom.
bIs there significant evidence that the slope of the line is not zero? Explain.
cIs there significant evidence that the straight line does not provide an appropriate fit? Explain.
dWrite a short note explaining what the inverse regression problem is, and why it is important in statistical analysis.
Hint
Statistics"Linear regression models are used to show or predict the relationship between two variables or factors, where the factor which is being predicted is known as the dependent variable and the factors that are used to predict the value of the dependent variable are known as the independent variables. Also, in simple linear regression, each observation consists of two values, one is for the ...
"Linear regression models are used to show or predict the relationship between two variables or factors, where the factor which is being predicted is known as the dependent variable and the factors that are used to predict the value of the dependent variable are known as the independent variables. Also, in simple linear regression, each observation consists of two values, one is for the dependent variable and the other one is for the independent variable. Generally, the simple linear regression analysis is the simplest form of a regression analysis that uses one dependent variable and one independent variable.