Question

The medical community unanimously agrees on the health benefits of regular exercise, but are adults listening? During each of the past 15 years, a polling organization has surveyed americans about their exercise habits. In the most recent of these polls, slightly over half of all American adults reported that they exercise for 30 or more minutes at least three times per week. The following data show the percentages of adults who reported that they exercise for 30 or more minutes at least three times per week during each of the 15 years of this study.

Year/Percentage of Adults Who Exercise 30 or more minutes at least three times per week

1 41.9

2 45.5

3 47.3

4 45.8

5 46.7

6 44.7

7 47.9

8 50.4

9 48.4

10 49.3

11 49.6

12 52.6

13 50.6

14 55.1

15 52.4

a. Does a linear trend appear to be present?

b.use simple linear regression to find the parameters for the line that minimizes MSE for this time series. Do not round your interim computations and round your final answers to four decimal places. For subtractive or negative numbers use a minus sign. (Example: -300)

y-intercept, b0 =

Slope, b1 =

MSE =

c.Use the trend equation from part (b) to forecast the percentage of adults next year (year 16 of the study) who will report that they exercise for 30 or more minutes at least three times per week. Do not round your interim computations and round your final answers to four decimal places. For subtractive or negative numbers use a minus sign. (Example: -300)

_%

d.Use the trend equation from part (b) to forecast the percentage of adults three years from now (year 18 of the study) who will report that they exercise for 30 or more minutes at least three times per week. Do not round your interim computations and round your final answers to four decimal places. For subtractive or negative numbers use a minus sign. (Example: -300) %

Answer 1

a)

There is a linear relationship between year and Percentage of Adults Who Exercise 30 or more minutes at least three times per week.

Explanation:

To see the relationship between year and Percentage of Adults Who Exercise 30 or more minutes at least three times per week, the scatter plot is obtained in excel by following these steps,

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: select year and % of Adults column then INSERT > Recommended Charts > Scatter > OK. The screenshot is shown below,

From the scatter plot we can observe that Percentage of Adults Who Exercise 30 or more minutes at least three times per week, increases linearly with year.

b)

Explanation:

The least square regression analysis is done in excel by following steps

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

Step 3: Select Input Y Range: '% of Adults' column, Input X Range: 'Year' column then OK. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

The least square estimate of regression coefficients and Mean square error values are,

c)

Explanation:

From the regression output summary, the regression equation is,

For Year = 16,

d)

Explanation:

From the regression output summary, the regression equation is,

For Year = 18,