Q 4.106 - Elementary Statistics

Question

a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)-(d).

b. Obtain the coefficient of determination.

c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer.

d. State how useful the regression equation appears to be for making predictions.

 Movie Grosses. The data  on domestic and overseas grosses for a random sample of 50 movies are on the WeissStats site.

Acreage and Value. The document Arizona Residential Property Valuation System, published by the Arizona Department of Revcaue, describes how county assessors use computerized systems to value single-family residential properties for property tax purposes. On the WeissStats site are data on lot size (in acres) and assessed value (in thousands of dollars) for a sample of homes in a particular area.

Step-by-Step Solution

Answer

a) Because the observations are scattered around a line in the scatterplot above, it is reasonable to find a regression line for the data. Because the observations are scattered around a line in the scatterplot above, it is reasonable to find a regression line for the data.

b) The coefficient of determination is 0.7264. 

c)As a result, the regression explains$72.64\%$ of the variation in the observed values of the response variable. It can be translated as the linear relationship between domestic grosses$\left(x\right)$ and abroad grosses$\left(y\right)$ accounts for $72.64\%$of the variability in overseas grosses.

d)Because the proportion of variation in the observed values of the response variable explained by the regression is $72.64\%$, which is larger than$50 \%$, the regression equation is useful in generating predictions.

Part a Step 1 Given Information

Given that  domestic and overseas grosses for a random sample of 50 movies are on the WeissStats site. 

Part a Step 2 Explanation

The scatterplot for the provided data can be drawn by using the MINITAB:

Step 1: Choose Graph$>$Scatterplot

Step 2: Choose With Connect Line, and then click OK.

Step 3: Under Y variables, enter a column of OVERSEAS

Step 4: Under X variables, enter a column of DOMESTIC

Step 5: Click OK

The scatterplot obtained will be

Because the observations are scattered around a line in the scatterplot above, it is reasonable to find a regression line for the data. Because the observations are scattered around a line in the scatterplot above, it is reasonable to find a regression line for the data.

Part b Step 1 Given Information

Given that  domestic and overseas grosses for a random sample of 50 movies are on the WeissStats site. 

Part b Step 2 Explanation

The coefficient of determination can be calculated by using MINITAB as follows:

Step 1: Choose Stat >Regression >Regression

Step 2: In Response, enter the column OVERSEAS

Step 3 : In Predictors, enter the column DOMESTIC

Step 4: Click OK

The MINITAB output will be:

As a result, the coefficient of determination is 0.7264.

Part c Step 1 Given Information

Given that  domestic and overseas grosses for a random sample of 50 movies are on the WeissStats site. 

Part c Step 2 Explanation

The coefficient of determination will be $0.7264$

As a result, the regression explains $72.64\%$ of the variation in the observed values of the response variable. It can be translated as the linear relationship between domestic grosses$\left(x\right)$and abroad grosses$\left(y\right)$ accounts for $72.64\%$the variability in overseas grosses.

Part d Step 1 Given Information

Given that  domestic and overseas grosses for a random sample of 50 movies are on the WeissStats site. 

Part d Step 2 Explanation

The correlation coefficient will be $0.7264$$0.7264.$

As a result, the regression explains $72.64\%$ of the variation in the observed values of the response variable. It can be translated as the linear relationship between domestic grosses $\left(x\right)$and abroad grosses $\left(y\right)$ accounts for $72.64\%$ of the variability in overseas grosses.

Because the proportion of variation in the observed values of the response variable explained by the regression is$72.64\%$, which is larger than $50\%$, the regression equation is useful in generating predictions.