**4.20 Neter, Kutner, Nachtsheim, and Wasserman (1996) Study**This study explores the relationship between the speed (y) at which an insurance innovation is adopted, the size of the firm (x), and the type of firm. The dependent variable y is the number of months between when the first firm adopted the innovation and when a particular firm adopted it. The firm's size x is measured in total assets (in millions), and the firm type is either mutual or stock.**Data Table:**- **Columns:** - **Number of Months Elapsed (y):** Time elapsed in months since the innovation was first adopted. - **Size of Firm (x, in millions):** Total assets of the firm. - **Type of Firm:** Indicates if the firm is mutual or stock.**Data Entries:**- Firms 1 to 10 are of "Mutual" type, and their elapsed months range from 17 to 16, with firm sizes from 151 to 290 million.- Firms 11 to 20 are of "Stock" type, and their elapsed months range from 28 to 14, with firm sizes from 164 to 305 million.**Tasks:**(a) Fit a model using only firm size as the independent variable (Model 1).(b) Interpret the coefficients in Model 1.(c) Create a regression model with firm size and type as independent variables (Model 2).(d) Plot showing the effect of firm type on the number of months elapsed.(e) Interpret the coefficients in Model 2.(f) Test for significant differences in months elapsed between mutual and stock firms at a 0.05 significance level, and find a 95% confidence interval (CI).(g) Estimate months elapsed for a firm with size 200 and type stock using Model 2, including 90% CI and prediction interval (PI).(h) Develop a model with size, type, and their interaction as variables (Model 3).(i) Interpret the coefficients in Model 3.(j) Perform a partial F-test comparing Model 2 (complete) to Model 1 (reduced) at a 0.05 level.This structured approach allows for understanding the impact of firm size and type on the adoption speed of innovations within insurance companies.

Answered: (a) Fit a model with just size of firm…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Question

**4.20 Neter, Kutner, Nachtsheim, and Wasserman (1996) Study**

This study explores the relationship between the speed (y) at which an insurance innovation is adopted, the size of the firm (x), and the type of firm. The dependent variable y is the number of months between when the first firm adopted the innovation and when a particular firm adopted it. The firm's size x is measured in total assets (in millions), and the firm type is either mutual or stock.

**Data Table:**

- **Columns:**
- **Number of Months Elapsed (y):** Time elapsed in months since the innovation was first adopted.
- **Size of Firm (x, in millions):** Total assets of the firm.
- **Type of Firm:** Indicates if the firm is mutual or stock.

**Data Entries:**
- Firms 1 to 10 are of "Mutual" type, and their elapsed months range from 17 to 16, with firm sizes from 151 to 290 million.
- Firms 11 to 20 are of "Stock" type, and their elapsed months range from 28 to 14, with firm sizes from 164 to 305 million.

**Tasks:**

(a) Fit a model using only firm size as the independent variable (Model 1).

(b) Interpret the coefficients in Model 1.

(c) Create a regression model with firm size and type as independent variables (Model 2).

(d) Plot showing the effect of firm type on the number of months elapsed.

(e) Interpret the coefficients in Model 2.

(f) Test for significant differences in months elapsed between mutual and stock firms at a 0.05 significance level, and find a 95% confidence interval (CI).

(g) Estimate months elapsed for a firm with size 200 and type stock using Model 2, including 90% CI and prediction interval (PI).

(h) Develop a model with size, type, and their interaction as variables (Model 3).

(i) Interpret the coefficients in Model 3.

(j) Perform a partial F-test comparing Model 2 (complete) to Model 1 (reduced) at a 0.05 level.

This structured approach allows for understanding the impact of firm size and type on the adoption speed of innovations within insurance companies.

Expert Solution

Step 1: Part a and b

Since you have posted a question with multiple subparts, we will provide solution to the first three sub-parts as per our Q&A guidelines. Please repost the remaining sub parts separately.

a) After entering the data in Excel go to Data>Data Analysis>Regression>choose the input range for Y and X and tick the "Labels" box>click "OK".

You get the following output:

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.840777
R Square	0.706906
Adjusted R Square	0.690623
Standard Error	5.231489
Observations	20

ANOVA
	df	SS	MS	F	Significance F
Regression	1	1188.167	1188.167	43.41371	3.45E-06
Residual	18	492.6326	27.36848
Total	19	1680.8

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	36.4821	2.844252	12.82661	1.71E-10	30.50656	42.45767	30.50656	42.45767
x	-0.0939	0.014257	-6.58891	3.45E-06	-0.12389	-0.06398	-0.12389	-0.06398

The equation of model 1 is:

$bold y with bold hat on top bold equals bold 36 bold. bold 4821 bold minus bold 0 bold. bold 0939 bold italic x$ , where $y with hat on top$ is the predicted number of months elapsed and x is the size of the firm (in millions).

b) In model 1, intercept = 36.4821 which is the average number of months elapsed for a firm with size of 0 million.

The slope coefficient is -0.0939. It means that for every extra million in size of the firm, the number of months elapsed decreases by 0.0939, on average.