Estimating income tax based on dividends is also not straightforward, due in part to Australia’s franking credit scheme. Mike is looking to simplify total annual tax projections for a share portfolio based simply on the share portfolio's current value. To do this, he wishes to determine if there is any statistically significant linear relationship between the two. Mike has randomly sampled 30 individuals with share portfolios over AUD$100,000 and mapped the assessed value of the portfolio (in AUD $1000) to the total taxes paid on that amount (in AUD$1). Mike's data is in the table below. Assessed Value Taxes 426.1 5014 368.8 3698 309.8 3691 373.9 5189 445.7 4455 505.1 5189 342.3 3416 343.6 3931 432.3 4393 329.2 3267 291.2 2871 399.3 4013 392.7 4728 482.2 4885 480.6 4888 390.8 3917 371.6 3738 311.9 3098 343.7 3633 304.7 3538 274.6 3427 457.1 4633 231.5 4009 450.5 4565 510.1 5946 308.4 3045 348.8 3504 410.4 3375 276.9 2706 337.5 4299 The linear regression equation is: Yi=_____+______Xi (Round to three decimal places as needed) b. Consider the Y-intercept, b0, and the slope, b1, calculated in part (a). Which of the following is most correct? A. The Y-intercept indicates the predicted total taxes for a portfolio with a value of $0. B. It is not appropriate to interpret the Y-intercept because it is outside the range of observed portfolio values. C. It is not appropriate to interpret the Y-intercept because a portfolio cannot have a value of $0. D. The Y-intercept indicates the predicted value for a portfolio with $0 in taxes. E. It is not appropriate to interpret the Y-intercept because a portfolio cannot be due $0 in total taxes. F. It is not appropriate to interpret the Y-intercept because it is outside the range of observed portfolio taxes. -------------------------------------------------------------------------- Which of the following is most correct? A. It is not appropriate to interpret the slope because there are no tax values with a difference of exactly $1. B. The slope indicates that for each increase of $1 in taxes, the predicted portfolio value is estimated to increase by a value equal to b1 times $1000. C. It is not appropriate to interpret the slope because there are no portfolio values with a difference of exactly $1000. D. The slope indicates that for each increase of $1000 in portfolio value, the predicted taxes are estimated to increase by a value equal to $b1. c. Use the regression equation developed in (a) to predict the mean total taxes for a portfolio whose assessed value is $450,000. Yi=$_____ (Round to the nearest dollar as needed.) d. Determine and consider the coefficient of determination, r2. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) A. r2=______ r could be positive or negative; however, for this question, it is less than r2. B. r2=____ r is always positive; however, for this question, it is greater than r2. C. r2=____ r could be positive or negative; however, for this question, it is greater than r2. D. r2=___ r is always positive; however, for this question, it is less than r2

Estimating income tax based on dividends is also not straightforward, due in part to Australia’s franking credit scheme. Mike is looking to simplify total annual tax projections for a share portfolio based simply on the share portfolio's current value. To do this, he wishes to determine if there is any statistically significant linear relationship between the two. Mike has randomly sampled 30 individuals with share portfolios over AUD$100,000 and mapped the assessed value of the portfolio (in AUD $1000) to the total taxes paid on that amount (in AUD$1). Mike's data is in the table below. Assessed Value Taxes 426.1 5014 368.8 3698 309.8 3691 373.9 5189 445.7 4455 505.1 5189 342.3 3416 343.6 3931 432.3 4393 329.2 3267 291.2 2871 399.3 4013 392.7 4728 482.2 4885 480.6 4888 390.8 3917 371.6 3738 311.9 3098 343.7 3633 304.7 3538 274.6 3427 457.1 4633 231.5 4009 450.5 4565 510.1 5946 308.4 3045 348.8 3504 410.4 3375 276.9 2706 337.5 4299 The linear regression equation is: Yi=_+Xi (Round to three decimal places as needed) b. Consider the Y-intercept, b0, and the slope, b1, calculated in part (a). Which of the following is most correct? A. The Y-intercept indicates the predicted total taxes for a portfolio with a value of $0. B. It is not appropriate to interpret the Y-intercept because it is outside the range of observed portfolio values. C. It is not appropriate to interpret the Y-intercept because a portfolio cannot have a value of $0. D. The Y-intercept indicates the predicted value for a portfolio with $0 in taxes. E. It is not appropriate to interpret the Y-intercept because a portfolio cannot be due $0 in total taxes. F. It is not appropriate to interpret the Y-intercept because it is outside the range of observed portfolio taxes. -------------------------------------------------------------------------- Which of the following is most correct? A. It is not appropriate to interpret the slope because there are no tax values with a difference of exactly $1. B. The slope indicates that for each increase of $1 in taxes, the predicted portfolio value is estimated to increase by a value equal to b1 times $1000. C. It is not appropriate to interpret the slope because there are no portfolio values with a difference of exactly $1000. D. The slope indicates that for each increase of $1000 in portfolio value, the predicted taxes are estimated to increase by a value equal to $b1. c. Use the regression equation developed in (a) to predict the mean total taxes for a portfolio whose assessed value is $450,000. Yi=$_ (Round to the nearest dollar as needed.) d. Determine and consider the coefficient of determination, r2. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) A. r2=__ r could be positive or negative; however, for this question, it is less than r2. B. r2= r is always positive; however, for this question, it is greater than r2. C. r2= r could be positive or negative; however, for this question, it is greater than r2. D. r2=_ r is always positive; however, for this question, it is less than r2

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Description: Estimating income tax based on dividends is also not straightforward, due in part to Australia’s franking credit scheme. Mike is looking to simplify total annual tax projections for a share portfolio based simply on the share portfolio's current

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Mike has randomly sampled 30 individuals with share portfolios over AUD$100,000 and mapped the assessed value of the portfolio (in AUD $1000) to the total taxes paid on that amount (in AUD$1). Mike's data is in the table below.

Assessed Value	Taxes
426.1	5014
368.8	3698
309.8	3691
373.9	5189
445.7	4455
505.1	5189
342.3	3416
343.6	3931
432.3	4393
329.2	3267
291.2	2871
399.3	4013
392.7	4728
482.2	4885
480.6	4888
390.8	3917
371.6	3738
311.9	3098
343.7	3633
304.7	3538
274.6	3427
457.1	4633
231.5	4009
450.5	4565
510.1	5946
308.4	3045
348.8	3504
410.4	3375
276.9	2706
337.5	4299

The linear regression equation is:

Yi=_____+______Xi

(Round to three decimal places as needed)

b. Consider the Y-intercept,

b0,

and the slope,

b1,

calculated in part (a).

Which of the following is most correct?

The Y-intercept indicates the predicted total taxes for a portfolio with a value of $0.

It is not appropriate to interpret the Y-intercept because it is outside the range of observed portfolio values.

It is not appropriate to interpret the Y-intercept because a portfolio cannot have a value of $0.

The Y-intercept indicates the predicted value for a portfolio with $0 in taxes.

It is not appropriate to interpret the Y-intercept because a portfolio cannot be due $0 in total taxes.

It is not appropriate to interpret the Y-intercept because it is outside the range of observed portfolio taxes.

--------------------------------------------------------------------------

Which of the following is most correct?

It is not appropriate to interpret the slope because there are no tax values with a difference of exactly $1.

The slope indicates that for each increase of $1 in taxes, the predicted portfolio value is estimated to increase by a value equal to b1 times $1000.

It is not appropriate to interpret the slope because there are no portfolio values with a difference of exactly $1000.

The slope indicates that for each increase of $1000 in portfolio value, the predicted taxes are estimated to increase by a value equal to $b1.

c. Use the regression equation developed in (a) to predict the mean total taxes for a portfolio whose assessed value is

$450,000.

Yi=$_____

(Round to the nearest dollar as needed.)

d. Determine and consider the coefficient of determination,

r2.

Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.)

r2=______

r could be positive or negative; however, for this question, it is less than

r2.

r2=____

r is always positive; however, for this question, it is greater than r2.

r2=____

r could be positive or negative; however, for this question, it is greater than

r2.

r2=___

r is always positive; however, for this question, it is less than r2.

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