Question

Location	Percent Obesity	Median Income
Alabama	33.5	49,936
Alaska	29.7	68,734
Arizona	28.9	62,283
Arkansas	35.9	49,781
California	24.7	70,489
Colorado	21.3	73,034
Connecticut	26.3	72,812
Delaware	30.7	65,012
District of Columbia	21.7	85,750
Florida	26.2	54,644
Georgia	30.5	55,821
Hawaii	22.1	80,108
Idaho	28.9	58,728
Illinois	29.3	70,145
Indiana	32.7	59,892
Iowa	30.9	68,718
Kansas	31.3	63,938
Kentucky	31.6	54,555
Louisiana	34.9	49,973
Maine	28.2	58,663
Maryland	29.6	86,223
Massachusetts	23.3	86,345
Michigan	30.7	60,449
Minnesota	27.6	71,817
Mississippi	35.5	42,781
Missouri	30.2	61,726
Montana	26.4	57,679
Nebraska	30.2	67,575
Nevada	27.7	61,864
New Hampshire	27.4	81,346
New Jersey	26.9	74,176
New Mexico	28.4	48,283
New York	27	67,274
North Carolina	29.7	53,369
North Dakota	32.2	66,505
Ohio	32.6	61,633
Oklahoma	33	54,434
Oregon	27.9	69,165
Pennsylvania	30.2	64,524
Rhode Island	27	62,266
South Carolina	32.1	57,444
South Dakota	29.8	59,463
Tennessee	31.2	56,060
Texas	31.9	59,785
Utah	25.7	77,067
Vermont	24.8	70,066
Virginia	28.5	77,151
Washington	27.3	79,726
West Virginia	35.7	50,573
Wisconsin	31.2	62,629
Wyoming	29.5	62,539

1. Add the regression line to your scatterplot and include the scatterplot with the regression line below and then answer the questions.

1. What is the equation for the regression line? This should be in the form shown, where a is the intercept and b is the slope: y=a+bx
2. Interpret the slope and the intercept for your equation. Does the interpretation for the intercept make sense for this data?
3. In 2018, the median household income for Kentucky was $54,555. Using the equation found in part a, what is the predicted obesity rate for Kentucky?
4. The actual obesity rate for Kentucky in 2018 was 31.6%. Calculate the residual.
5. Puerto Rico, a United States territory, had a median household income of $20,296 in 2018. Should we use this equation to predict the percent obesity for Puerto Rico in 2018? Why or why not? What is this kind of prediction called?

Answer 1

Here, we have to add the regression line to your scatterplot and include the scatterplot with the regression line below and then answer the questions.

To draw the scatterplot we run the following steps in Minitab-

1. Enter the data in two columns.

2. Select "Graph" then "Scatterplot" then with "regression".

3. Select percent obesity in Y and Median income in X.

4. Click OK.

After running the above steps we get-

Scatterplot of Percent obesity vs Median income 36 34 32 30 Percent obesity 28 26 24 22 20 40000 50000 80000 90000 60000 70000 Median income

a) To find the regression equation we run the following steps in minitab-

Steps for regression-

1. Enter the given values in different columns

.2. Go to “Stat” then “Regression” then “Regression” then “Fit regression model”.

3. Enter Percent obesity in “response” and Median income in “continuous predictor”.

4. Select storage then check the box of residuals.

5. Click OK.

After running the following steps we get the output as-

Percent obesity = 44.06 - 0.000230 Median income

b) Slope = -0.000230 which means if there is one unit increase in the median income the percent obesity decreases by 0.000230%

Intercept = 44.06 which means that the origin shifts 44.06 units in positive direction.

Here, in this scenario we see if the median income reduces to zero then the intercept represents the mean value of the precent obesity.

c) In 2018, the median household income for Kentucky was $54,555. Using the equation found in part a, we have to find what is the predicted obesity rate for Kentucky.

So in the equation we put median income = 54555 and get the corresponding obesity percent = 44.06-0.000230*54555 = 31.51235

d) The actual obesity rate for Kentucky in 2018 was 31.6%. We have to calculate the residual.

From the steps done in minitab we get the residual value for Kentucky as 0.10469.