Question
In: Statistics and Probability
Given below are seven observations collected in a regression study on two variables, x (independent variable)...
Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2 Given the followings b1 = -1.13 SSR = 50.625 SSE= 9.376 Sb1 = .2165 a. At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero. (No excel please show steps thank you)
Solutions
Expert Solution
Step:1 State the Hypotheses:- If there is a significant linear relationship between the independent variable X and the dependent variable Y, the slope will not equal zero. Ho: Β1 = 0 H1: Β1 ≠ 0 The null hypothesis states that the slope is equal to zero, and the alternative hypothesis states that the slope is not equal to zero. Degrees of freedom. For simple linear regression (one independent and one dependent variable), the degrees of freedom (DF) is equal to: DF = n - 2 where n is the number of observations in the sample. Based on the above table, the following is calculated: Step:2 Test statistic:- The test statistic is a t statistic (t) defined by the following equation. t = b_1-Β1/SE but, Ho: Β1 = 0 Therefore, t = b1 / SE where, b1:The slope of the simple regression line. SE:The standard error of the regression slope. test statistics= t = b1 / SE = -1.125/0.216506 = -5.1962 t_table = 2.5706 we are ready to compute the margin of error : me:Margin of error. me=t_table*se = 2.5706*0.216506 = 0.5566 Then we calculate the confidence interval for regression slope: CI=([b_1-me,b_1+me])=[-1.6816 -0.5684] p_value = 0.0035 Step:3 Decision:- if p_value is less than the significance level 0.05 then we are rejecting the null hypothesis,otherwise we accept it. Step:4 Conclusion:- we are rejecting null hypothesis there is a significant linear relationship between the independent variable X and the dependent variable Y
orchestra answered 2 years agoRelated Solutions
Given below are seven observations collected in a regression study on two variables, x (independent variable)...
Given below are seven observations collected in a regression
study on two variables, x (independent variable) and y (dependent
variable)
X
Y
2
12
3
9
6
8
7
7
8
6
7
5
9
2
a. develop the least squares estimated regression equation
b. At 95% confidence, perform a t test
and determine whether or not the slope is significantly different
from 0
c.Compute the coefficient of determination
d. Develop the 95% confidence interval for the mean value of...
Given below are seven observations collected in a regression study on two variables, X (independent variable)...
Given below are seven observations collected in a regression
study on two variables, X (independent variable) and Y (dependent
variable).
X
Y
2
12
3
9
6
8
7
7
8
6
7
5
9
2
a. Develop the least squares estimated regression equation.
b. State the hypotheses to test for the significance of the
regression line.
c. Perform an F test to determine whether or not the model is
significant. Let α = 0.05.
A) A sample of 13 observations collected in a regression study on two variables, x(independent variable)...
A) A sample of 13 observations collected in a regression study
on two variables, x(independent variable) and y(dependent
variable). The sample resulted in the following data.
summation (x_i-xbar)2=14, summation
(x_i-xbar)(y_i-ybar)=72, xbar=3, ybar=10
Calculate the y-intercept (b_0) of the estimated regression
equation.
B) A sample of 9 observations collected in a regression study on
two variables, x(independent variable) and y(dependent variable).
The sample resulted in the following data.
summation (x_i-xbar)2=14, summation
(x_i-xbar)(y_i-ybar)=79, xbar=3, ybar=10
Calculate the slope of the estimated regression equation.
a) A sample of 8 observations collected in a regression study on two variables, x(independent variable)...
a) A sample of 8 observations collected in a regression study on
two variables, x(independent variable) and y(dependent variable).
The sample resulted in the following data.
SSR=66, SST=86
Calculate an unbiased estimate of the variance
of the error term epsilon.
b) A sample of 11 observations collected in a regression study
on two variables, x(independent variable) and y(dependent
variable). The sample resulted in the following data.
SSE=22, SSR=64
Calculate the coefficient of determination for the developed
estimated regression equation.
c)...
3.) Given are five observations collected in a regression study on two variables. 2 6 9...
3.) Given are five observations collected in a regression study
on two variables.
2
6
9
13
20
7
18
9
26
23
Develop a scatter diagram for these data.
Develop the estimated regression equation for these data.
Use the estimated regression equation to predict the value of
y when x=6
17.) The data from exercise 3 follow.
2
6
9
13
20
7
18
9
26
23
The estimated regression equation for these data is . What
percentage of...
Given are five observations collected in a regression study on two variables. xi 2 6 9...
Given are five observations collected in a regression study on
two variables.
xi
2
6
9
13
20
yi
7
18
8
26
21
(a)
Develop the estimated regression equation for these data.
ŷ =
Use the estimated regression equation to predict the value of
y when
x = 20.
Given are five observations for two variables, x and y. The estimated regression equation for these...
Given are five observations for two variables, x and y. The
estimated regression equation for these data is y = 1 + 2.4x
(A) Compute SSE, SST, and SSR
(B) Compute the coefficient of determination, R^2.
(C) Compute the sample correlation coefficient.
x
y
1
3
2
8
3
5
4
12
5
13
In a multi linear regression case study, the dependent variable is house_value, the independent variables are...
In a multi linear regression case study, the dependent variable
is house_value, the independent variables are house_age,
crime_rate, tax_rate, trying to build a model to predict the house
value, how to state model assumptions? What's the assumption in
this case? Thanks!
The estimated regression equation for a model involving two independent variables and 65 observations is: yhat...
The estimated regression equation for a model involving two
independent variables and 65 observations is:
yhat = 55.17+1.1X1 -0.153X2
Other statistics produced for analysis include: SSR = 12370.8, SST
= 35963.0, Sb1 = 0.33, Sb2 = 0.20.
(16 points)
Interpret b1 and b2 in this estimated
regression equation
Predict y when X1 = 65 and X2 = 70.
Compute R-square and Adjusted R-Square.
Comment on the goodness of fit of the model.
Compute MSR and MSE.
Compute F and use...
The estimated regression equation for a model involving two independent variables and 65 observations is: yhat...
The estimated regression equation for a model involving two
independent variables and 65 observations is:
yhat = 55.17+1.1X1 -0.153X2
Other statistics produced for analysis include: SSR = 12370.8, SST
= 35963.0, Sb1 = 0.33, Sb2 = 0.20.
(16 points)
Interpret b1 and b2 in this estimated
regression equation
Predict y when X1 = 65 and X2 = 70.
Compute R-square and Adjusted R-Square.
Comment on the goodness of fit of the model.
Compute MSR and MSE.
Compute F and use...
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