Background and Content:

As far as market research is concerned there are three different types of research including exploratory, descriptive and causal research. Causal research is concerned with finding the relationship between variables and ascertaining whether there is any cause-effect relationship between variables. There could be a number of variables included in a study, however, simple regression analysis considers only two variables and investigates the relationship between them.

Within recent weeks and due to COVID-19 there has been a recession in the market and in particular in the car industry. Using causal market research, a dealer is interested in finding the relationship between the price of a new car and the amount of power (kw) it has. For this purpose, he designs a survey and asks potential customers to fill in the survey for him. In the process of data collection, he collects the data for a range of new cars and he conducts linear regression analysis with Excel. Results of the analysis is presented in the following tables:

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.94

R Square 0.88

Adjusted R Square 0.87

Standard Error 2605.35

Observations 20

ANOVA

df SS MS F Significance F

Regression 1 8.8608 8.8608 130.5464 0.000

Residual 18 1.2208 6787853

Total 19 1.0109

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 4815.80 2121.57 2.27 0.04 358.55 9273.06

Power 106.38 9.31 11.43 0.00 86.82 125.94

Assessment Tasks:

Answer all questions below:

You are required to establish whether there is any relationship between the price and the amount of the power (kw) in the car by answering the following questions:

1. State the linear regression equation for this data.

2. Interpret the meaning of the slope,in this problem.

3. Predict the mean price of a car with power of 300 kW.

4. In there any meaningful relationship between car price and power?

5. Determine the coefficient of determination, (R2 ) and interpret its meaning.