Homework Answers
a. The correlation coefficient between is 0.6744533.
cor(x,y)
[1] 0.6744533
b. The regression coefficients are Bo = 0.7143 and B1 = 1.5714.
summary(fit)
Call:
lm(formula = y ~ x)
Residuals:
1 2 3 4 5
-2.2857 0.1429 1.2857 -0.2857 1.1429
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.7143 1.4046 0.509 0.646
x 1.5714 0.9932 1.582 0.212
Residual standard error: 1.662 on 3 degrees of freedom
Multiple R-squared: 0.4549, Adjusted R-squared:
0.2732
F-statistic: 2.503 on 1 and 3 DF, p-value: 0.2117
c. The regression line equation is Y^= B0^ + B1^ * X. = 0.7143 + 1.5714*X.
d.The value of Y when X=8 is 13.28571.
predict(fit,data.frame(x=8),interval = "confidence")
fit lwr upper
1 13.28571 -8.336957 34.90839
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The following information regarding a dependent variable (Y in $1000) and an independent variable (X) is...
The following information
regarding a dependent variable (Y in $1000) and an independent
variable (X) is provided.
Y
Dependent Variable
15
17
23
17
I. The least-squares estimate of the slope
equals:
II. The least-squares estimate of the intercept
equals:
III. If the independent variable increases by 2
units, the dependent variable is expected to
a. decrease by $300
b. decrease by $3000
c. decrease by $3
d. decrease by $2
e. none of the above
The letter corresponding...
The following information regarding a dependent variable (Y in $1000) and an independent variable (X) is...
The following information regarding a dependent variable (Y in
$1000) and an independent variable (X) is provided.
Y
Dependent Variable
15
17
23
17
I. The least-squares estimate of the slope
equals:
II. The least-squares estimate of the intercept
equals:
III. If the independent variable increases by 2
units, the dependent variable is expected to
a. decrease by $300
b. decrease by $3000
c. decrease by $3
d. decrease by $2
e. none of the above
The letter corresponding...
The data shown below for the dependent variable, y, and the independent variable, x, have been...
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Let r be the correlation coefficient. Denote the explanatory variable by X and the responsible variable...
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14. Multiple Choice Variables x and y have a correlation coefficient of r = 0.89. Which...
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The following information
regarding a dependent variable (Y in $1000) and an independent
variable (X) is provided.
Y
Dependent Variable
15
17
23
17
I. The least-squares estimate of the slope
equals:
II. The least-squares estimate of the intercept
equals:
III. If the independent variable increases by 2
units, the dependent variable is expected to
a. decrease by $300
b. decrease by $3000
c. decrease by $3
d. decrease by $2
e. none of the above
The letter corresponding...
The following information regarding a dependent variable (Y in
$1000) and an independent variable (X) is provided.
Y
Dependent Variable
15
17
23
17
I. The least-squares estimate of the slope
equals:
II. The least-squares estimate of the intercept
equals:
III. If the independent variable increases by 2
units, the dependent variable is expected to
a. decrease by $300
b. decrease by $3000
c. decrease by $3
d. decrease by $2
e. none of the above
The letter corresponding...
The data shown below for the dependent variable, y, and the independent variable, x, have been collected using simple random sampling. X 10 15 11 19 18 17 5 17 18 y 9070 30 8020 30 5060 40 40 a. Develop a simple linear regression equation for these data. b. Calculate the sum of squared residuals, the total sum of squares, and the coefficient of determination c. Calculate the standard error of the estimate. d. Calculate the standard error for...
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