Question

2.146  Sales and production. Refer to the previous two exercises.

1. (a) Make a scatterplot with sales as the response variable and production as the explanatory variable. Describe the relationship. Are there any outliers or influential observations?

2. (b) Find the least-squares regression line and add it to your plot.

3. (c) Interpret the slope of the line in the context of this exercise.

4. (d) Interpret the intercept of the line in the context of this exercise. Explain whether or not this interpretation is useful in explaining the relationship between these two variables.

5. (e) What is the predicted value of sales for a country that has an index of 109 for production?

6. (f) The Netherlands has an index of 109 for production. Find the residual for this country.

7. (g) What percent of the variation in sales is explained by production? How does this value compare with the percents of variation that you calculated in the two previous exercises?

Here the previous two exercises for the data ;

meis

2.144  Dwelling permits and sales for 23 countries. The Organisation for Economic Co-operation and Development collects data on main economic indicators (MEIs) for many countries. Each variable is recorded as an index with the year 2000 serving as a base year. This means that the variable for each year is reported as a ratio of the value for the year divided by the value for 2000. Use of indices in this way makes it easier to compare values for different countries. Table 2.3 gives the values of three MEIs for 23 countries.³¹

1. (a) Make a scatterplot with sales as the response variable and permits issued for new dwellings as the explanatory variable. Describe the relationship. Are there any outliers or influential observations?

2. (b) Find the least-squares regression line and add it to your plot.

3. (c) Interpret the slope of the line in the context of this exercise.

4. (d) Interpret the intercept of the line in the context of this exercise. Explain whether or not this interpretation is useful in explaining the relationship between these two variables.

5. (e) What is the predicted value of sales for a country that has an index of 224 for dwelling permits?

   TABLE 2.3 Dwelling Permits, Sales, and Production for 21 Countries

   Country	Dwelling permits	Sales	Production
   Australia	116	137	109
   Belgium	125	105	112
   Canada	224	122	101
   Czech Republic	178	134	162
   Denmark	121	126	109
   Finland	105	136	125
   France	145	121	104
   Germany	54	100	119
   Greece	117	136	102
   Hungary	109	140	155
   Ireland	92	123	144
   Japan	86	99	109
   Korea	158	110	156
   Luxembourg	145	161	118
   Netherlands	160	107	109
   New Zealand	127	139	112
   Norway	125	136	94
   Poland	163	139	159
   Portugal	53	112	105
   Spain	122	123	108
   Sweden	180	142	116

6. (f) Canada has an index of 224 for dwelling permits. Find the residual for this country.

7. (g) What percent of the variation in sales is explained by dwelling permits?

meis

2.145  Dwelling permits and production. Refer to the previous exercise.

1. (a) Make a scatterplot with production as the response variable and permits issued for new dwellings as the explanatory variable. Describe the relationship. Are there any outliers or influential observations?

2. (b) Find the least-squares regression line and add it to your plot.

3. (c) Interpret the slope of the line in the context of this exercise.

4. (d) Interpret the intercept of the line in the context of this exercise. Explain whether or not this interpretation is useful in explaining the relationship between these two variables.

5. (e) What is the predicted value of production for a country that has an index of 224 for dwelling permits?

6. (f) Canada has an index of 224 for dwelling permits. Find the residual for this country.

7. (g) What percent of the variation in production is explained by dwelling permits? How does this value compare with the value that you found in the previous exercise for the percent of variation in sales that is explained by building permits?

Answer 1

Simple linear regression

2.146.

a. We put the data in Minitab and select the option Graph and then Scatter plot to get the following output:

From the plot we get no clear relationship between the two variables.

There is an outlier in the data and that is related to sales 161 and production 118.

b. We go to the Regression option to get the following output:

Thus the least square regression line is:

Sales= 112.26+ 0.11* Production.

Adding it to the plot we get:

c. The slope is 0.11. It means that for every one unit increase in production, sales will be increased by 0.11 units.

d. The intercept is 112.26. This implies that when production is equal to zero then the sales is 112.26 units. This interpretation is not useful as practically it can't happen.