Question

Use the given data set to complete parts (a) through (c) below. (Use a = 0.05.) 5 х у 10 9.14 8 8.14 13 8.73 9 8.76 11 9.26 14 8.09 6 6.13 4 3.09 12 9.13 7 7.25 4.73 Click here to view a table of critical values for the correlation coefficient. a. Construct a scatterplot. Choose the correct graph below. OA. OB. O c. OD y AY 10- 8- Ay 10-1 a 10- 10- 8- 6- 8-1 8- 6- 6- 6- 4- 4- 4- 4- 3 2 2- 2- 0- 2 0- 0 0- 0 0 4 8 12 16 4 8 0 8 4 8 12 16 12 16 12 16 b. Find the linear correlation coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. The linear correlation coefficient is r= (Round to three decimal places as needed.) Using the linear correlation coefficient found in the previous step, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below. O A. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables. OB. There is sufficient evidence to support the claim of a linear correlation between the two variables. OC. There is insufficient evidence to support the claim of a linear correlation between the two variables. OD. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables. c. Identify the feature of the data that would be missed if part (b) was completed without constructing the scatterplot. Choose the correct answer below.

Answer 1

a. Construct a scatter plot:

Bring data in to excel sheet.

Select both x and y variable and insert the scatter plot chart.

Option A is correct

А B с D E F G - H J K L 1 X y 10 8 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 10 8 13 9 11 14 6 4 12 7 5 9.14 8.14 8.73 8.76 9.26 8.09 6.13 3.09 9.13 7.25 4.73 6 4. 2 0 0 4 8 12 16

b. Linear correlation coefficient r = 0.816

(Excel formula)

E4 X fx =CORREL(A2:A12,B2:B12) А B C E F C у 1 x 2 3 r= 0.816 4 5 6 7 8 9 10 11 10 8 13 9 11 14 6 4 12 7 5 9.14 8.14 8.73 8.76 9.26 8.09 6.13 3.09 9.13 7.25 4.73 12 13

we have to run a regression analysis to find , is there a significant correlation exists between the variable or not

Go to data tab --> choose data analysis --> choose regression

Get & Transform Data Queries & Connections Data Types Sort & Filter K14 fx Significance F1 Regression ? X Input OK Input Y Range: $B$1:$B$12 1 А B с Cancel X y Input X Range: $A$1:$A$12 1 1 2 3 4 Help Labels Constant is Zero Confidence Level: 95 96 5 Output options 6 $F$4 1 7 10 8 13 9 11 14 6 4 12 7 5 9.14 8.14 8.73 8.76 9.26 8.09 6.13 3.09 9.13 7.25 4.73 8 9 10 11 12 13 14 15 16 O Qutput Range: O New Worksheet Ply: O New Workbook Residuals Residuals Standardized Residuals Residual Plots Line Fit Plots Normal Probability Normal Probability Plots

Result:

A с E F G H - J K L M N w X у SUMMARY OUTPUT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 10 8 13 9 11 14 6 4 12 7 5 9.14 8.14 8.73 8.76 9.26 8.09 6.13 3.09 9.13 7.25 4.73 Regression Statistics Multiple R 0.815682221 R Square 0.665337486 Adjusted R Square 0.628152763 Standard Error 1.240182294 Observations 11 ANOVA df Significance F 0.0022 1 Regression Residual SS MS F 27.52000364 27.52 17.89276 13.84246909 1.538052 41.36247273 9 10 Total Intercept х Coefficients 2.993818182 0.500181818 Standard Error t Stat P-value 1.128002027 2.654089 0.026299 0.118246742 4.229984 0.002207 Lower 95% Upper 95%ower 95.0%pper 95.0% 0.442100317 5.545536 0.4421 5.545536 0.232689104 0.767675 0.232689 0.767675

Significance F is nothing but P-value

P-value = 0.0022

If the p-value is less than the significance level (α=0.05):

• Decision: Reject the null hypothesis.
• Conclusion: "There is sufficient evidence to conclude that there is a significant linear relationship between x and y because the correlation coefficient is significantly different from zero."

Option B.

There is sufficent evidence to support the claim of a linear correlation between the two variables.

(c) identify the feature of the data that would be missed in part b

Option c

The scatterplot reveals a distince pattern that is a straight -line pattern woth positive slope