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Law of Supply: You will need to use software to answer these questions. The Law

ID: 3052637 • Letter: L

Question

Law of Supply: You will need to use software to answer these questions.

The Law of Supply states that an increase in price will result in an increase in the quantity supplied (assuming all other factors remain unchanged). Below is the scatterplot, regression line, and corresponding data for price (x) -vs- quantity supplied (y).

You should be able to copy and paste the data by highlighting the entire table.

Answer the following questions regarding the relationship.

(a) Using all 12 data pairs for x and y, calculate the correlation coefficient. Round your answer to 3 decimal places.
r = _______

(b) Is there a significant linear correlation between these variables?

Yes

No    


(c) Use software to find the regression equation. What is the slope and y-intercept? Round each answer to one decimal place.


(d) Use the regression equation to estimate the quantity supplied if the price is set at $5.00. Round your answer to the nearest whole number.
? = ______ units

          index Price (x) Supply (y) 1 3.00 309 2 4.00 239 3 4.25 552 4 4.75 355 5 5.00 385 6 5.00 360 7 6.50 775 8 6.75 672 9 8.00 884 10 8.00 1025 11 9.50 1069 12 10.00 928 Supply Data 1200r 3 1000 800 L 3 Quantity Supplied 3 3 400 F 200 F . 10 12 Price per item (in dollars)

Explanation / Answer

      

   A)The correlation Between Price and Supply is 0.9200

          B)YES,

               There is Significant linear Correlation Between Price and Supply as The test statistic of

Pearson's product-moment correlation is 7.42 and p-value is 0.000025 less than 0.05.As the Alternative Hypothesis for this test is : true correlation is not equal to 0

         C) Using R Software The Estimate of Coefficients of Simple linear Regression is

Slope (Price)

   122.595

y-intercept

-134.249   

                d) The Supply is 478.726 Units When Price is $5

              ? = 478.726 units

> Price=law[,2]

> Supply=law[,3]

> corr=cor.test(Price,Supply)

> model=lm(Supply~Price,data=law)

> coeff=round(model$coefficients,3)

> x=c(1,5)

> Supply_5=x%*%coeff

> law

   index.. Price Supply

1        1 3.00    309

2        2 4.00    239

3        3 4.25    552

4        4 4.75    355

5        5 5.00    385

6        6 5.00    360

7        7 6.50    775

8        8 6.75    672

9        9 8.00    884

10      10 8.00   1025

11      11 9.50   1069

12      12 10.00    928

> corr

        Pearson's product-moment correlation

data: Price and Supply

t = 7.4234, df = 10, p-value = 2.253e-05

alternative hypothesis: true correlation is not equal to 0

95 percent confidence interval:

0.7332514 0.9776918

sample estimates:

      cor

0.9200028

> summary(model)

Call:

lm(formula = Supply ~ Price, data = law)

Residuals:

    Min      1Q Median      3Q     Max

-163.70 -99.58    8.11   84.69 178.49

Coefficients:

            Estimate Std. Error t value Pr(>|t|)   

(Intercept) -134.25     108.89 -1.233    0.246   

Price         122.60      16.51   7.423 2.25e-05 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 123.6 on 10 degrees of freedom

Multiple R-squared: 0.8464,   Adjusted R-squared: 0.831

F-statistic: 55.11 on 1 and 10 DF, p-value: 2.253e-05

> coeff

(Intercept)       Price

   -134.249     122.595

> Supply_5

        [,1]

[1,] 478.726

index Price Supply 1 3 309 2 4 239 3 4.25 552 4 4.75 355 5 5 385 6 5 360 7 6.5 775 8 6.75 672 9 8 884 10 8 1025 11 9.5 1069 12 10 928