S121 STA510 BUSINESS STATISTICS

Download data (in excel format) for PRIVATE GROSS FIXED CAPITAL FORMATION - MACHINERY AND EQUIPMENT (GFCF) and GROSS DOMESTIC PRODUCT (GDP) for the period March 1986 to December 2020 from the above website to carry out Tasks 2-6. Display a screenshot of first 10 rows of the dataset

(a) Describe the movements of two data series GFCF and GDP.

(b) Analyze the relationship between the two variables, GFCF and GDP.

When one variable could cause or depend on the value of other variable we can say the variables are related. We use scatter diagram to analyze the relationship between two variable, between two variable GFCF and GDP, the trend line is upward sloping and there is a positive linear relationship, if GFCF increase GDP also increase and if GFCF decrease the GDP will also decrease.

3(a) summarize the above two data series, GFCF and GDP

Comment on the strength and the direction of the relationship between GFCF and GDP

We use the correlation coefficient r to measure the strength and direction of a linear relationship between two variable .The values of correlation coefficient r is always between -1 to +1.The correlation coefficient we found is 0.874226152 .We consider values more than +0.70 a strong upward trending (positive) linear relationship and Exactly +1. A perfect upward trending (positive) linear relationship .As our value falls between +0.70 and +1 we can understand the correlation coefficient is strong and upward trending.

4 (a) develop a model to explain the relationship between GFCF and GDP. Explain the reason for your choice of the dependent and independent variables of your model

Dependent variable usually falls in the Y axis and independent variable is usually falls in the X axis ,GFCF is independent and GDP is dependent variable ,in data when the GFCF increase the GDP also increase as we seen in 2a ,

A straight-line model with one independent variable is referred as a simple linear regression model,

Linear regression line Y=β0 + β1x, Y is dependent variable, β0 is y intercept and β1 is the slope and independent variable. In our model both β0 and β1x are population parameter which are usually unknown and estimated from sample data.

4 B (b) estimate the model you proposed in 4(a) using Excel

We use data analysis from data ribbon and for using data analysis function we must need to install data analysis tool pack prior to using data analysis, after accessing to data analysis we need to use the regression function input the range and we will get the summary output

Interpret the estimated coefficients you obtained in 4(b).

β1= -21.06 β0= -42990

If there is no production =0 in GFCF in private sector the gdp will be -42990million which is hypothetical and not possible in real life ,

If capital formation increase 1 million gdp will increase 21.06 million.

Applying appropriate statistical techniques,

(a) test whether the linear relationship between Gross Fixed Capital Formation - Machinery and Equipment and Gross Domestic Product you estimated in Q4 is significant (use  = 0.05). (Hint: display 6 steps process in relation to this test).

When we test hypothesis we need to construct 6 steps, we use z test when we know the population variance, when we do not know population variance we use T test, we need to demonstrate using hypothesis whether there is a linear relationship present between GFCF and GDP , From 2 to 4 we do not know the population variation only we know sample variance . so using the standard test statistic we will use t test ,

Step 1 : State the null and alternate hypothesis

: β1 =0 (no linear relationship)

: β1≠ 0 (linear relationship)

Step 2: Determine the test statistics sigma square is unknown we use T test , T test formula

Tcalc =r-beta 1

Devided by rootover 1 –r sqare devided by n-2

Tcalc =Beta not divided by se

Step 3: Specify the significance level

Alpha is equal = 0.05

It is two tail test so the alpha will be divided by 2

Step 4 : define the decision rule

If the p value is less than α , null hypothesis will be rejected , if the α we will not reject the null hypothesis ,

Step 5: Calculate the value of test statistics

From excel we found that the t test value is 20.53

T value 20.53 and degree of freedom 130 er jonno P value is determined from excel 0.00332441

Step 6: Make a decision and answer the question

P value (0.000000) is less than significance level 0.05 we will reject the null hypothesis, so there is a linear relationship between GFCF and GDP

(B)Assess the fitness of the estimated model you have estimated in Q4.

We determine fitness of model by square ( CO efficient of determination ) the value ranges between 0 to 1 .From R square we determine of variation of two data , Rsquare measures the proportion of variation in y that is explained by the variation of x , the bigger the value of r squate the more the data fit more with dataset

From the excel we found that r square is equal is 0.76 or 76 percent , so 76 percent of the variation in gdp is explained by the variation of the GFCF .

6. Based on all your answers above, write a summary report about your findings to hand over to your team leader (maximum 250 words).