1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Fed [463]
2 years ago
15

According to industry sources, online banking is expected to take off in the near future. The projected number of households (in

millions) using this service is given in the following table. (Here, x = 0 corresponds to the beginning of 1997.)
Year, x 0 1 2 3 4 5
Households, y 4.5 7.5 10.0 13.0 15.6 18.0
(a) Find an equation of the least-squares line for these data. (Give numbers to three decimal places.)
y(x) =

(b) Use your result of part (a) to estimate the number of households using online banking at the beginning of 2007, assuming the projection is accurate.

Mathematics
1 answer:
Airida [17]2 years ago
5 0

Answer:

(a) The least-square regression line is: y=4.662+2.709x.

(b) The number of households using online banking at the beginning of 2007 is 31.8.

Step-by-step explanation:

The general form of a least square regression line is:

y=\alpha +\beta x

Here,

<em>y</em> = dependent variable

<em>x</em> = independent variable

<em>α</em> = intercept

<em>β</em> = slope

(a)

The formula to compute intercept and slope is:

\begin{aligned}        \alpha  &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2}  \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2}        \end{aligned}

The values of ∑<em>X</em>, ∑<em>Y</em>, ∑<em>XY</em> and ∑<em>X</em>² are computed in the table below.

Compute the value of intercept and slope as follows:

\begin{aligned}        \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} =             \frac{ 68.6 \cdot 55 - 15 \cdot 218.9}{ 6 \cdot 55 - 15^2} \approx 4.662 \\ \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2}        = \frac{ 6 \cdot 218.9 - 15 \cdot 68.6 }{ 6 \cdot 55 - \left( 15 \right)^2} \approx 2.709\end{aligned}

The least-square regression line is:

y=4.662+2.709x

(b)

For the year 2007 the value of <em>x</em> is 10.

Compute the value of <em>y</em> for <em>x</em> = 10 as follows:

y=4.662+2.709x

  =4.662+(2.709\times10)\\=4.662+27.09\\=31.752\\\approx 31.8

Thus, the number of households using online banking at the beginning of 2007 is 31.8.

You might be interested in
Choose the correct measure of an astronomical unit. 9.3 million miles .93 million miles 93 million miles 930 million miles
Genrish500 [490]
By definition, an astronomical unit in miles is given by:
 1 AU = 9.3 * 10 ^ 7 miles&#10;
 As it is in exponential notation, then we must rewrite.
 9.3 * 10 ^ 7 = 93,000,000 miles&#10;
 Therefore, an astronomical unit is:
 93 million miles
 Answer:
 
93 million miles
8 0
2 years ago
Solve the following simultaneous linear equations.<br>2x + y = 5<br>4x – 3y = -10​
Jet001 [13]

Answer:

(1/2,4)

Step-by-step explanation:

First, determine y in first equation: 2x+y=5 or  y=5-2x

replace value of y determined in first equation (5-2x) into 2nd equation    

4x-3(5-2x)=-10

4x-15+6x=10

10x=5

x=1/2

put value of x into either equation to solve for y so

2(1/2)+y=5

1+y=5

y=4

answer: x=1/2, y=4

check answer by substituting x and y into either equation:

4x-3y=-10

4(1/2)-3(4)=-10

2-12=-10

-10=-10

or

2x+y=5

2(1/2)+4=5

1+4=5

5=5

7 0
3 years ago
When csc(O)sin(0) is simplified, what is the result?
Olin [163]

Answer:

This is not my answer, it was done by another expert in Brainly.

We are given:  

csc (0) * sin (0)  

This is to be simplified using trigonometric identities:  

csc (x) = 1/sin(x)  

so, csc (0) = 1/sin(0)  

then,  

1/sin(0) * sin (0), the result will be sin(0) / sin (0) which is equal to 1.  

Therefore, the answer is 1.

3 0
2 years ago
5 | 61251 is this true or false?
slamgirl [31]

Step-by-step explanation:

the answer is false because its counting by 5

3 0
2 years ago
Solve the quadratic equation numerically (using tables of x- and y-values).
Stells [14]

Answer:

Third Option: x=6 or x=-3

Step-by-step explanation:

x^2+9x+18=0

(x+6)(x+3)=0

x=6 or x=-3

3 0
2 years ago
Other questions:
  • Solve the system by the elimination method? -5x-2y=2 6x-2y=24
    11·2 answers
  • Solve the equation. Check your answer. If necessary, round to 3 decimal places<br> In x = -2, x=
    7·1 answer
  • Positive skewness of a distribution could be caused by which of the following choices:
    10·1 answer
  • Help on number 7 and 8 please
    12·1 answer
  • Write the first five terms in the sequence defined by the explicit formula
    5·2 answers
  • If f (x)=3x-2 and g(x) =6-4 find f(x) + g(x)
    15·1 answer
  • Fill in the table using this function rule.<br> y = 24 - 4x<br> x y<br> 2 ?<br> 3 ?<br> 4 ?<br> 6 ?
    8·2 answers
  • The temperature is 15°F and is expected to fall 2°F each hour during the night.expression​
    11·1 answer
  • ANSWER QUICK PLEASE CORRECTLY !!!!!!! WILL MARK BRIANLIEST ANSWER !!!!!!!!!!!!!!!!!!
    12·1 answer
  • 13 The enrollment at Eldridge Middle School has been tracked for two years. The enrollment was 1,648 students in 2015. The table
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!