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
cupoosta [38]
3 years ago
14

An automobile dealer wants to see if there is a relationship between monthly sales and the interest rate. A random sample of 4 m

onths was taken. The results of the sample are presented below. Monthly Sales (Y) Interest Rate (In Percent) (X) 22 9.2 20 7.6 10 10.4 45 5.3 a) Use the method of least squares to compute an estimated regression line. b) Obtain a measure of how well the estimated regression line fits the data.
Mathematics
1 answer:
SVETLANKA909090 [29]3 years ago
6 0

Answer:

a) y=-6.254 x +75.064  

b) r =-0.932

The % of variation is given by the determination coefficient given by r^2 and on this case -0.932^2 =0.8687, so then the % of variation explained by the linear model is 86.87%.

Step-by-step explanation:

Assuming the following dataset:

Monthly Sales (Y)     Interest Rate (X)

       22                               9.2

       20                               7.6

       10                                10.4

       45                                5.3

Part a

And we want a linear model on this way y=mx+b, where m represent the slope and b the intercept. In order to find the slope we have this formula:

m=\frac{S_{xy}}{S_{xx}}  

Where:  

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}  

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}  

With these we can find the sums:  

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=278.65-\frac{32.5^2}{4}=14.5875  

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=696.9-\frac{32.5*97}{4}=-91.225  

And the slope would be:  

m=\frac{-91.225}{14.5875}=-6.254  

Nowe we can find the means for x and y like this:  

\bar x= \frac{\sum x_i}{n}=\frac{32.5}{4}=8.125  

\bar y= \frac{\sum y_i}{n}=\frac{97}{4}=24.25  

And we can find the intercept using this:  

b=\bar y -m \bar x=24.25-(-6.254*8.125)=75.064  

So the line would be given by:  

y=-6.254 x +75.064  

Part b

For this case we need to calculate the correlation coefficient given by:

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

r=\frac{4(696.9)-(32.5)(97)}{\sqrt{[4(278.65) -(32.5)^2][4(3009) -(97)^2]}}=-0.937  

So then the correlation coefficient would be r =-0.932

The % of variation is given by the determination coefficient given by r^2 and on this case -0.932^2 =0.8687, so then the % of variation explained by the linear model is 86.87%.

You might be interested in
Solve: |v + 8| − 5 = 2
AveGali [126]

Answer:

v¹= -15, v²= -1

Step-by-step explanation:

there's 2 solutions to this

3 0
3 years ago
Read 2 more answers
What is the multiplicative identity matrix? What is it similar to in the set of real numbers? Explain your answer
bagirrra123 [75]

Answer:

An identity matrix, is a matrix that have '1' in the main diagonal. All of the other terms are '0'. When you multiply any matrix by the identity matrix, the result is the same matrix that you multiplied.

Example:

\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]

In the set of the real number is the same that the application of identity property.

Every number multiplied by 1 es the same number.

Step-by-step explanation:

7 0
3 years ago
Helpppp thanksssss!!!!!
Molodets [167]
Money of account is 58.19+2.74__60.85
6 0
3 years ago
Please help will mark you brainliest. ( all links will be reported)
cestrela7 [59]

Answer:

$6.22

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
You play a game that involves spinning a wheel. Each section of the wheel shown has the same area. Use a sample space to determi
Anastasy [175]

Answer:

is it fighet spinner or I am wrong hahahaa fighet spinner

7 0
3 years ago
Read 2 more answers
Other questions:
  • The map below shows the path that Jin walked this morning. According to his pedometer, the total distance of this path was 2.3 k
    6·1 answer
  • H e l p m e
    14·1 answer
  • FILL IN THE BLANKS: PLEASE HELP ASAP
    7·1 answer
  • Whats the greatest common factor for 12,30,72?
    7·2 answers
  • Let h(x)=2x+5hand g(x)=8-3xg, What is the value of h(g(1.5)
    8·1 answer
  • Describe and correct the error a student made when solving the equation 7=-4(x+7)-3+2x. What is the correct solution?
    11·1 answer
  • Y-intercept = 4.5 and slope = -2.5<br> equation: y =<br> X +
    12·1 answer
  • An audio books club charges an initial joining fee of $20.00. The cost per audio book is $15.00. The graph shows the cost of bel
    10·2 answers
  • The temperature overnight in Sitka, Alaska was 12 below zero. How should this be written?
    6·1 answer
  • Explain or show how you could find by using the value of 5⋅3. If needed, use this diagram to support your reasoning.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!