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
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 928Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.