QUESTION 16 Determine the margin of error that would be used to estimate the slo

Question

QUESTION 16

Determine the margin of error that would be used to estimate the slope for a least squares simple linear regression model if the (standard error) estimate of the standard deviation of the slope (sb1) was 1.57, there were 26 (n) observations in the data set for the sample, and the desired level of significance (alpha) is 0.02. Use the appropriate critical value of t, to four decimals, and do not round any other values in your calculations. Enter your response to 2 decimals (i.e. 2.12).

QUESTION 17

Determine the upper limit of the confidence interval to estimate the slope for a least squares simple linear regression model if the slope coefficient from the sample is 1.2, the (standard error) estimate of the standard deviation of the slope (sb1) is 0.96, there were 27 observations in the data set for the sample, and the desired level of significance (alpha) is 0.05. Use the appropriate critical value of t, to four decimals, in your calculations and do not round intermediate steps. Enter your response to 2 decimals (i.e. 2.12).

QUESTION 18

Assume you have conducted a simple linear regression analysis of profit amount by sales amount and the interval estimate of the slope coefficient is from -0.20 to 0.60. Choose the following that represents what should be concluded from the analysis.

fail to reject the null hypothesis and conclude that the slope may be zero (average profit per unit increase in sales may be zero for the population of sales from which this sample was selected)

fail to reject the null hypothesis and conclude that the slope is not zero (average profit per unit increase in sales is greater than zero for the population of sales from which this sample was selected)

reject the null hypothesis and conclude that the slope may be zero (average profit per unit increase in sales may be zero for the population of sales from which this sample was selected)

reject the null hypothesis and conclude that the slope is not zero (average profit per unit increase in sales is greater than zero for the population of sales from which this sample was selected)

all of these are true

none of these are true

QUESTION 19

Determine the value of the residual for a least squares simple linear regression model where the predicted value of y (y-hat) is 84.18, for a given value of x, and the observed value of y from the sample is 69.08. formula 14.10

Enter your response to 2 decimals (i.e. 2.12). Include the negative sign, if appropriate.

QUESTION 20

In a regression analysis, the error term (epsilon) is a random variable with a mean or expected value of

zero

one

any positive value

any value

1.

fail to reject the null hypothesis and conclude that the slope may be zero (average profit per unit increase in sales may be zero for the population of sales from which this sample was selected)

2.

fail to reject the null hypothesis and conclude that the slope is not zero (average profit per unit increase in sales is greater than zero for the population of sales from which this sample was selected)

3.

reject the null hypothesis and conclude that the slope may be zero (average profit per unit increase in sales may be zero for the population of sales from which this sample was selected)

4.

reject the null hypothesis and conclude that the slope is not zero (average profit per unit increase in sales is greater than zero for the population of sales from which this sample was selected)

5.

all of these are true

6.

none of these are true

Explanation / Answer

16)

here for (n-2=24) degree of freedom and 0.02 level; critical value of t =2.4922

therefore margin of error =t* Sb1=3.91

17)here for (n-2=25) degree of freedom and 0.05 level; critical value of t =2.0595

therefore upper confidence level =estimated slope + t*std error =3.18

18)

fail to reject the null hypothesis and conclude that the slope may be zero (average profit per unit increase in sales may be zero for the population of sales from which this sample was selected)

19)

residual =y-yhat=69.08-84.18=-15.1

20)

zero

1.

zero

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