1. Assume we estimate a simple linear regression line based on 31 observations.
ID: 3069132 • Letter: 1
Question
1. Assume we estimate a simple linear regression line based on 31 observations. Select the appropriate error degrees of freedom needed to create a confidence interval for the slope.
a. 30
b. 29
c. 27
d. 28
2. Assume we estimate a simple linear regression line based on 31 observations. Select the appropriate critical value (t*) needed to create a 95% confidence interval for the slope.
a. 2.052
b. 2.048
c. 2.045
d. 2.042
3. The following question is based on a simple linear regression model between x and y. Assume you want to determine if there is significant evidence to suggest that as the explanatory variable x increases there is a tendency on average for the response variable y to decrease. Which of the following is the best choice for a null and alternative hypothesis?
a. Ho: b1 = 0
Ha: b1 < 0
b. Ho: B1 = 0
Ha: B1 < 0
c. Ho: B1 = 0
d. Ho: B1 = 0
Ha: B1 > 0
e. Ho: b1 = 0
4. The following question is based on a simple linear regression model between explanatory variable x and response variable y. Assume a 95% confidence interval for the population slope is the following 0.75 to 1.25. Based on this interval which of the following is NOT a possible population relationship between x and y.
a. Joe proposes that for every 100 unit increase in x the average response will increase by 120 units.
b. Vivian proposes that for every 300 unit increase in x the average response will increase by about 200 units.
c. Kari proposes that for every 400 unit increase in x the average response will increase by about 350 units.
d. Quinn proposes that for every 200 unit increase in x the average response will increase by 220 units.
5. The following question is based on a simple linear regression model between explanatory variable x and response variable y. Assume a 95% confidence interval for the population slope is the following: Lower bound of 0.75 and upper bound of 1.95. Based on this interval what is the margin of error for this example.
a. 0.6
b. 0.3
c. 1.2
d. 1.35
6. In a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the _____ come from a normal distribution.
a. Response Variable
b. Explanatory Variable
c. Observations
d. Errors
7. Which of the plots is most important to check the assumption related to the form of a simple linear regression model?
a. Scatterplot of residuals by the predicted value
b. Scatterplot of the response by the explanatory variable
c. Normal Quantile Plot of the Residuals
d. Scatterplot of the residuals by the response variable
8. A diamond shape in a residual plot suggests a violation of which assumption?
a. constant variance
b. normality
c. form of the model
d. independence of observations
Explanation / Answer
1)
error degrees of freedom =n-2=31-2 =29 option B
2)
critical value (t*) needed to create a 95% confidence interval for the slope =2.045
option C
3)
b. Ho: B1 = 0
Ha: B1 < 0
4)
b. Vivian proposes that for every 300 unit increase in x the average response will increase by about 200 units.
5)
margin of error =(upper -lower bound)/2 =(1.95-0.75)/2 =0.6 ; option A
6)d. Errors
7)
c. Normal Quantile Plot of the Residuals
8)
a. constant variance ( please check normality if this one comes wrong and revert)
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