Need answers and work shown for all the following questions:

1. The following are eight observations collected in a research study on the possible relationship between an independent x and a dependent variable y. (6 Points)

Xi	13	19	18	24	21	26	15
yi	36	54	46	65	51	67	41

1. Develop a scatter diagram for these data
2. Develop the estimated regression equation for these data.
3. Use the estimated regression equation to predict the value of y given x = 16

Please note that you can either use the formula (12.6) and (12.6), a statistical package such as StatTools, or the Regression program within Excel?s Data Analysis Add-in to calculate the estimated regression

2. Given the following output obtained from a regression analysis of the dependent variable Sales and an independent variable Advertising(10 Points)

ANOVA
	df	SS	MS
Regression	1	13489.58	13489.58
Residual	15	45620.74	3041.38
Total	16	59110.32
	Coefficients	Standard Error
Intercept	254.1	54.2
Advertising	0.14	0.066

1. Use the p-value approach to perform a F test for the significance of the linear relationship between Advertising and Sales at the 0.05 level of significance
2. Calculate the coefficient of determination
3. What percentage of the variability of Sales can be explained by its linear relationship with Advertising? What is the sample correlation coefficient?
4. What is the estimated regression equation?
5. Use the critical value approach to perform a t test for the significance of the linear relationship between Advertising and Sales at the 0.05 level of significance

3. You may want to refer to the description of the Regression Analysis output from Excel in the Appendix of Chapter 12 before completing the following question.

The data inBUSI1013-Regression A.XLSX(SEE FILE ATTACHED) is collected for building a regression model to estimate value of residential homes in a mid-size Canadian city. Use this data to perform a simple regression analysis between Value and Size. (12 Points)

1. Develop a scatter diagram using Value as the dependent variable y and size as the independent.
2. Develop the estimated regression equation.
3. Use the estimated regression equation to predict the value of an 1850 square-foot home.
4. Use the critical-value approach to perform a F test for the significance of the linear relationship between Value and Size at the 0.05 level of significance.
5. What percentage of the variability of Value of residential homes can be explained by its linear relationship with Size?
6. Use the p-value approach to perform a t test for the significance of the linear relationship between Value and Size at the 0.05 level of significance.

4. The estimated regression equation for a model involving two independent variables and 15 observations is:

yhat = 29.75 - 0.57X₁+ 2.53X₂

Other statistics produced for analysis include: SSR=8120.3, SST=8835.5, S_b1=0.085, S_b2=0.35 (16 Points)

1. Interpret b₁and b₂in this estimated regression equation
2. Predict y when X₁=48 and X₂=115
3. Compute R and R_a
4. Comments on the goodness of fit of the model
5. Compute MSR and MSE
6. Compute F and use it to test whether the overall model is significant using a p-value (?=0.05)
7. Perform a t test for the significance of ?₁. Use a level of significance of 0.05
8. Perform a t test for the significance of ?₂. Use a level of significance of 0.05

5. Use data inBUSI1013-Regression A.XLSX(SEE FILE ATTACHED)to complete the following. You will need to use a statistical package such as StatTools or the Regression program within Excel?s Data Analysis Add-in to generate the estimated regression equation and the ANOVA etc. (12 Points)

1. What is the estimated regression equation using Value as the dependent variable and Size as well as Number of Bedrooms as the independent variable?
2. Comments on the goodness of fit of the model Using the coefficient of determination
3. Conduct F test to see whether the overall model is significant. Use ?=0.05.
4. Perform a t test for the significance of the Size variable. Use ?=0.05.
5. Perform a t test for the significance of the Number of Bedrooms variable. Use ?=0.05.
6. Estimate the value of a three-bedroom home that has 1850 square feet of space.

Value 400.0 708.0 661.0 570.0 463.0 485.0 494.0 565.0 487.0 500.0 498.0 633.0 579.0 449.0 672.0 657.0 519.0 Size 1206 2393 2382 2149 1451 1525 1589 1919 1413 1416 1530 2348 1890 1308 2294 2334 1590 Number of Bedrooms 2.0 4.0 4.0 4.0 3.0 3.0 3.0 4.0 3.0 4.0 3.0 5.0 3.0 3.0 5.0 5.0 2.0 487.0 640.0 640.0 465.0 509.0 498.0 585.0 1764 2151 2523 1413 1499 1557 1775 3.0 3.0 4.0 3.0 3.0 3.0 3.0 676.0 2216 3.0 569.0 701.0 561.0 675.0 691.0 559.0 399.0 589.0 506.0 503.0 422.0 628.0 700.0 516.0 575.0 668.0 588.0 577.0 673.0 504.0 629.0 443.0 1924 2500 2118 2340 2437 1948 1288 1897 1453 1682 1307 2329 2365 1420 1862 2389 2145 1924 2374 1787 2236 1259 3.0 5.0 4.0 4.0 4.0 5.0 2.0 3.0 4.0 3.0 3.0 4.0 4.0 4.0 4.0 4.0 5.0 4.0 4.0 3.0 4.0 2.0 608.0 728.0 639.0 651.0 622.0 562.0 682.0 553.0 578.0 465.0 719.0 611.0 2246 2510 2155 2397 2126 1678 2465 2058 2205 1574 2512 2239 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 3.0 5.0 3.0