Y= duration of residence in that city

H0 = rXY=0 i.e there is NO relationship between the 2 continuous variables X and Y Ha ≠0, there is a relationship between the 2 continuous variables X and Y Analyze -> correlate -> bivariate

The SPSS output indicates that rXY has a value of .936. Clearly this value of rxy seems different from zero. However the question that arises is whether this value of rxy is statistically different from zero at 95% level of confidence.

There is a significant relationship between these two variables at 95% confidence as p-value is at .000 which is below 0.05. Hence we are therefore unable to retain H0 and thus we accept HA. Thus, we can infer at 95% level of confidence that in this sample, there is indeed a significant relationship between the two variables X and Y (i.e rXY is indeed different from zero). Assuming that this sample is a good representation of the target population, we extend this inference even to the target population. Hence, even in the target population there is indeed a significant positive relationship between the two variables X and Y (i.e rXY is indeed different from zero).

2. Multiple regression write up

y= attitude towards the city of residence (dependent variable) x1 = duration of residence in the city (1st independen variable) x2= importance associated with the weather in the city (2nd IV)

The initial model is: Y = β1 + β2.X1+ β3.X2

Step 1:

H0: R2= 0 i.e none of the independent variables X1 and X2 have a significant relationship with the dependent variable Y i.e. both β2 and β3 are equal to zero

HA: R2 ≠ 0 i.e At least one of the independent variables X1 and X2 have a significant relationship with the dependent variable Y i.e. at least one of the two,β2 and β3 are NOT equal to zero

The SPSS output indicates that R2 has a value of .945. This value does seem different from zero. However, we need to confirm is whether this R2 is indeed different from zero, in this sample at 95% confidence.

The SPSS output also indicates that the F statistic for the R2 has a value of 77.29 and its associated p-value is .000 (i.e. less than .05). given this, we are unable to retain H0 and hence we accept HA. We thus infer at 95% confidence level that in this sample R2 is indeed different from zero i.e at least one fo the two namely β2 and β3 are NOT equal to zero in this sample. Assuming that this sample is a good representation of the target population, we extend this inference (that at least one of the two, namely β2 and β3, is Not equal to zero) even to the target population.

Step 2:

H0: β1 = 0

HA : β1 ≠ 0

The SPSS output indicates that β1 has a value of .337. This value seems different from zero, but we note that it is quite close to zero. However, what we need to check is whether β1is different from zero in this sample, at 955 level of confidence.

The SPSS output also indicates that the t-statistic for β1 has a value of .595 and its associated p-value is .567 (i.e larger than .05). Hence we retain H0. We therefore infer at 95% level of confidence that in this sample, β1 = 0. Assuming that this sample is a good representation of the target population, we extend this inference( that, β1 = 0) holds even in the target population.

Step 3.

H0: β2 = 0 i.e the independent variable X1 does NOT have a significant relationship with the dependent variable Y

HA: β2 ≠0 I.e. the independent variable X1 has a significant relationship with the dependent variable Y

The SPSS output indicates that B2 has a value of .481. This value seems different from zero, though we note that it is quite close to zero. So, we need to check whether B2 is different from zero in this sample, at 95% level of confidence.

The SPSS output also indicates that the t-statistic for B2 has a value of 8.16 and its associated p-value is .000 (i.e less than .05) Hence we are unable to retain H0 and thereby accept HA. Hence we infer at 95% level of...