please urgent!!

Question

The table below shows the national debt of Canada since 1962. Enter the data ( use 1962 as year 0) then use your calculator to determine which type of regression equation produces the line of best fit. Use the grid below to draw an accurate scatterplot and line of best fit and answer the questions related to this data. I need a graph for this too :) 

 

NATIONAL DEPT OF CANADA

YEAR || BILLIONS OF DOLLARS

1962 | 14.8

1971 | 20.3

1981 | 91.9

1991 | 377.7

1997 | 562.9

2002 | 511.9

2008 | 457.6

2009 | 463.7

2010 | 519.1

2011 | 551.4

 

a) what is your regression equation for this data? ( Round values to the nearest thousandth) What does each of the two variables in your equation reprsent?

b) Use your regression analysis to predict the national dept of Canada in the year 2020.

c) Use your regression analysis to predict the national dept of Canada in the year 2030.

d) Use your regression analysis to determine which year the national dept will surpass one trillion dollar. Please Explain how you determined this answer.

 

Thank you so much:)

Answer 1

(a)

Regression analysis investigates the relationship between variables; typically, the relationship between a dependent variable and one or more independent variables .

We use linear regression when we have a continuous outcome variable (Y) and we want to explore how Y changes as a function of one or more predictors (X).

So here in this case we use linear regression .

The equation for  linear regression is  y = a + b x .

Now we have to calculate values for a and b .

The  national debt of Canada can be tabulated as shown below .

S.no	Year (x)	Billions of dollar (y)	xy	x²	y²
1	0 (1962)	14.8	0	0	219.04
2	9 (1971)	20.3	182.7	81	412.09
3	19 (1981)	91.9	1746.1	361	8445.61
4	29 (1991)	377.7	10953.3	841	142657.29
5	35 (1997)	562.9	19701.5	1225	316856.41
6	40 (2002)	511.9	20476	1600	262041.6
7	46 (2008)	457.6	21049.6	2116	209397.76
8	47 (2009)	463.7	21793.9	2209	215017.69
9	48 (2010)	519.1	24916.8	2304	269464.81
10	49 (2011)	551.4	27018.6	2401	304041.96
∑	322	3571.3	147838.5	13138	1728554.25

 

Comments

continue ...... 

     From the above table, Σx = 322, Σy = 3571.3, Σxy = 147838.5, Σx2 = 13138, Σy2 = 1728554.25 , number of samples n = 10 .

  y = -24.70 + 11.86 x . 

  So the regression equation is y = -24.70 + 11.86 x .

The scatterplot is 

Answer 2

(b)

The regression equation is y = -24.70 + 11.86 x .

National dept of canada in the year 2020 [After 58 years] means x = 58 .         [since 1962 treated as 0]

                                     y (2020) = -24.70 + 11.86 (58)

                                                 = -24.70 + 687.88

                                                 = 663.18

So the  National dept of canada in the year 2020 is 663.18 billions of dollars .

Answer 3

(c)

The regression equation is y = -24.70 + 11.86 x .

National dept of canada in the year 2030 [After 68 years] means x = 68 .         [since 1962 treated as 0]

                                     y (2020) = -24.70 + 11.86 (68)

                                                 = -24.70 + 806.48

                                                 = 781.78

So the  National dept of canada in the year 2020 is 781.78 billions of dollars .

Answer 4

(d)

The regression equation is y = -24.70 + 11.86 x .

The national dept will exceeds the one trillion dollars , means y = 1000 billions of dollars .

                   1000 = -24.70 + 11.86 x 

                   1024.7 = 11.86 x

                    x = 1024.7 / 11.86 

                    x = 86.399

So After 87 years the national dept of canada will cross one trillion dollars .

year is 1962 + 87 = 2049

So in the year 2049 , the national dept of canada will cross one trillion dollars .