Number for graph:
19,15,43,39,35,31,27,22,18,14,42,38,17,17,13,41,41

y = 1.754 + 1.001 x

Step-by-step explanation:

The equation of Regression equation is of the form of:

y = a + bx

where, a is intercept and b is slope

The formula for a and b is given by,

Thus, a = 1.754

and b = 1.001

Thus, Regression Line is given by,

y = 1.754 + 1.001 x

Now plotting these line:

Step-by-step explanation:

Given

The x and y values

Required

The regression line equation

Because of the length of the given data, I will run the analysis using online tools, then analyze the result.

From the analysis, we have:

--- Sum of squares

--- Sum of products

The regression equation is calculated as:

Where:

So, we have:

So:

becomes

y = 1.754 + 1.001 x

Step-by-step explanation:

The equation of Regression equation is of the form of:

y = a + bx

where, a is intercept and b is slope

The formula for a and b is given by,

Thus, a = 1.754

and b = 1.001

Thus, Regression Line is given by,

y = 1.754 + 1.001 x

Now plotting these line:

Step-by-step explanation:

H0: u = 150

H1: u ≠ 150

Total sum = 15933.24

N = 100

Mean = 15933.24/100

= 159.3324

σ² = 25954.03 - (159.3324)²/100

σ² = 556.213

σ = √556.213

σ = 23.8162

Testing hypothesis

t = (bar x - u)/ σ/√n

= 159.3324-150/23.8162/√100

= 3.91

We will have a p value of 0.02

0.0002 < 0.01

We reject null hypothesis at 1% level of significance

C. Mean = 159.3324

Se= 2.3936

Df = 100-1 = 99

Critical value at 0.01 = +-2.626

T = x-u/s.e

= -2.626 =( x -150)/2.3936

When we cross multiply and solve this

X = 143.714 for the lower tail

2.626 = (x-159)/2.3936

= 156.286 for upper tail.

We therefore reject H0 at

Bar X <= 143.71

Bar X >= 156.286

At 10%

Critical t = 1.660

-1.660 = (x - 150)/2.3936

Solving this ,

X =146.02 at the lower tail

1.660 = (x-150)/2.3936

X = 153.97

We reject H0 at

X<= 146.03

X>=153.97

Step-by-step explanation:

H0: u = 150

H1: u ≠ 150

Total sum = 15933.24

N = 100

Mean = 15933.24/100

= 159.3324

σ² = 25954.03 - (159.3324)²/100

σ² = 556.213

σ = √556.213

σ = 23.8162

Testing hypothesis

t = (bar x - u)/ σ/√n

= 159.3324-150/23.8162/√100

= 3.91

We will have a p value of 0.02

0.0002 < 0.01

We reject null hypothesis at 1% level of significance

C. Mean = 159.3324

Se= 2.3936

Df = 100-1 = 99

Critical value at 0.01 = +-2.626

T = x-u/s.e

= -2.626 =( x -150)/2.3936

When we cross multiply and solve this

X = 143.714 for the lower tail

2.626 = (x-159)/2.3936

= 156.286 for upper tail.

We therefore reject H0 at

Bar X <= 143.71

Bar X >= 156.286

At 10%

Critical t = 1.660

-1.660 = (x - 150)/2.3936

Solving this ,

X =146.02 at the lower tail

1.660 = (x-150)/2.3936

X = 153.97

We reject H0 at

X<= 146.03

X>=153.97

HCA

a. HCA's Liabilities-to-assets ratios and times-interest-earned ratios in the years 2005 through 2009:

1. Liabilities-to-assets ratios = Total liabilities/Total Assets

                  Dec. 09     Dec. 08    Dec. 07     Dec. 06     Dec. 05

                 136.63%     141.60%    143.18%     147.51%     78.12%

2. Times-interest-earned ratios = EBIT/Interest Expense

                  Dec. 09     Dec. 08      Dec. 07       Dec. 06       Dec. 05

                 1.91 times  1.45 times   1.33 times    2.76 times   4.11 times

b. The percentage decline in EBIT that HCA could have suffered each year between 2005 and 2009 to make it unable to make interest payments out its operating earnings, where operating earnings is defined as EBIT:

                  Dec. 09     Dec. 08      Dec. 07       Dec. 06       Dec. 05

                 191%            145%           133%            276%         411%

c. The volatility of HCA's cash flows over the period 2005 to 2009:

The standard deviation of the cash flows (cash and cash equivalents) is 115, showing that there is so much volatility in the cash flows.

d. HCA's return on invested capital (ROIC) in the years 2005 - 2009:

= Net Income - Dividend / Total Liabilities + Equity x 100

ROIC =                        4.37%      2.77%      3.64%        4.38%     6.41%

Explanation:

a) Data and Calculations:

HCA INC

ANNUAL INCOME STATEMENT

($ MILLIONS, EXCEPT PER SHARE)

                                  Dec. 09    Dec. 08     Dec. 07     Dec. 06     Dec. 05

Sales                         $ 30,052  $ 28,374  $ 26,858   $ 25,477  $ 24,455

Cost of Goods Sold     24,826     24,023     22,480       21,448      20,391

Gross Profit                   5,226         4,351        4,378        4,029       4,064

Depreciation                  1,425          1,416        1,426          1,391         1,374

Operating Profit            3,801         2,935       2,952        2,638       2,690

Interest Expense           1,987         2,021        2,215           955          655

Non-Operating

 Income/Expense           188            256           661             179           412

Pretax Income             2,002           1,170        1,398         1,862       2,327

Total Income Taxes       627            268            316           625          725

Minority Interest            321             229           208           201           178

Net Income             $ 1,054           $ 673       $ 874      $ 1,036    $ 1,424

ANNUAL BALANCE SHEET

ASSETS                   Dec. 09    Dec. 08     Dec. 07     Dec. 06     Dec. 05

Cash & Equivalents  $ 312        $ 465       $ 393       $ 634       $ 336

Net Receivables      3,692         3,780       3,895        3,705       3,332

Inventories                 802            737            710           669          616

Other Current

 Assets                     1,771           1,319        1,207          1,070          931

Total Current

 Assets                   6,577         6,301       6,205         6,078       5,215

Gross Plant, Property

 & Equipment      24,669       23,714     22,579       21,907     20,818

Accumulated

 Depreciation       13,242       12,185        11,137       10,238       9,439

Net Plant, Property

 & Equipment       11,427        11,529      11,442        11,669      11,379

Investments

 at Equity                 853            842         688            679         627

Other Investments 1,166         1,422       1,669         1,886       2,134

Intangibles            2,577        2,580      2,629         2,601      2,626

Deferred Charges   418           458          539             614           85

Other Assets          1,113          1,148          853             148          159

TOTAL ASSETS  24,131      24,280     24,025       23,675    22,225

LIABILITIES

Long Term Debt Due

In One Year          846          404           308             293         586

Accounts

 Payable            1,460         1,370         1,370            1,415       1,484

Taxes Payable      -               224            190                -              -

Accrued

 Expenses      2,007           1,912          1,981           1,868       1,825

Total Current

 Liabilities       4,313           3,910        3,849          3,576      3,895

Long Term

 Debt          24,824        26,585      27,000         28,115      9,889

Deferred Taxes -                  -                -                  390         830

Minority

 Interest       1,008              995          938             907          828

Other

Liabilities    2,825           2,890        2,612          1,936        1,920

TOTAL LIA-

 BILITIES   32,970         34,380     34,399       34,924       17,362

Preferred

 Stock            147                155           164             125                -

Common

 Stock               1                     1                1                 1                4

Capital

 Surplus      226                 165            112                 -                -

Retained

 Earnings (9,213)          (10,421)     (10,651)       (11,375)       4,859

Common

 Equity     (8,986)        (10,255)     (10,538)      (11,374)       4,863

TOTAL

 EQUITY  (8,839)         (10,100)     (10,374)      (11,249)       4,863

TOTAL LIABILITIES &

EQUITY $24,131      $ 24,280  $ 24,025   $ 23,675  $ 22,225

ii) Liabilities-to-assets ratio:

                                  Dec. 09    Dec. 08     Dec. 07     Dec. 06     Dec. 05

Liabilities                    32,970      34,380     34,399       34,924       17,362

Assets                         24,131      24,280     24,025       23,675     22,225

                                 136.63%     141.60%    143.18%     147.51%     78.12%

iii) Times Interest Earned:

Operating Profit           3,801         2,935       2,952        2,638       2,690

Interest Expense          1,987         2,021        2,215           955          655

                                1.91 times   1.45 times 1.33 times  2.76 times 4.11 times

iv) Volatility:  This is the degree of change of the cash flows, showing its tendency to change from one period to the other.  As calculated, the volatility is very high, showing that the cash flows have higher risk of change.  See below:

                                  Dec. 09    Dec. 08     Dec. 07     Dec. 06     Dec. 05

Cash & Equivalents     $ 312      $ 465        $ 393         $ 634       $ 336

Mean = $428

Deviation from mean     -116            37            -35             206          -92

Squared deviation      13,456       1,369         1,225       42,436      8,464

Sum of squared deviation = 66,950

Mean = 13,390

Square root of mean or Standard Deviation = 115

v) Return on Invested Capital = Net Income/Total liabilities + Equity

                               Dec. 09    Dec. 08     Dec. 07     Dec. 06     Dec. 05

Net Income             $ 1,054        $ 673       $ 874      $ 1,036    $ 1,424

TOTAL LIABILITIES &

EQUITY                  $24,131  $ 24,280  $ 24,025   $ 23,675  $ 22,225

ROIC =                        4.37%      2.77%      3.64%        4.38%     6.41%

The estimated value of the Batting Average is 0.229.

Step-by-step explanation:

In this case regression analysis is to performed to determine if there is a significant linear relationship for Batting Averages with Runs Score, Doubles, Triples, Home Runs and Strike Outs.

The independent and dependent variables are as follows:

y = Batting Averages

x₁ = Runs Score/Times at Bat

x₂ = Doubles/Times at Bat

x₃ = Triples/Times at Bat

x₄ = Home Runs/Times at Bat

x₅= Strike Outs/Times at Bat

The regression analysis can be performed in Excel.

Consider the regression output attached.

The regression equation is as follows:

Now estimate the Batting Average when Run Score (x₁) = 0.123, Doubles ( x₂) = 0.040, Triples (x₃) = 0.0045 ,  Home Runs ( x₄) = 0.009 and Strike Outs (x₅) = 0.189 as follows:

Thus, the estimated value of the Batting Average is 0.229.